Wait, you need some special documents to sign up? you might ask.
Yes. When signing up for the next event you will need to enter two codes that can only be found in said set. There are three ways to acquire them.

1 & 2) Order the set online from circle.ms.
At the top of their site there should be a tab saying "通販・商品一覧".
At the time of writing, it looks like this:

If you order the physical set (which is cheaper), you'll get an A4-ish sized envelope in the mail from circle.ms, containing the sign-up pamphlet. The online set option is fairly new, so I have yet to try it myself. However, it says the comiket registration can be started directly after purchase, and the two codes will be shown at the order confirmed page. Also, the codes will be linked to your current account and cannot be transferred.

3) Buy the set at the previous comiket.
The comiket official booths in most halls should be selling them throughout the duration of the market.

I bought mine in advance from circle.ms, and it looks like this.

Inside you'll find an invoice containing the two codes necessary for registration.

Yes, I did both cover and mosaic my codes to be safe.
The set also contains everything needed for mail sign-up, but we'll be doing it online so just ignore all that.

Now then, head to circle.ms again and choose the "ｲﾍﾞﾝﾄ新規/申込中一覧" tab.
The next comiket at the time of writing is C97, so it looks like this, but it'll probably look different for C98 and later.

The first one is regular registration. The one below is for having two circles share one table (usually one space = half a table) and can only be done after both circles have finished the normal registration. I will not be covering this option in this guide.

next you'll end up at a page showing the event information, the rules and guidelines (run those through google translate to see) and the circle cut templates (A and B). Circle cuts are the images for each circle printed in the catalogue and on the online map. Important: leave the little square in the upper corner completely blank. Do not cover it or the side frames what so ever.

The one on the bottom is for the manga report and cannot be used as a circle cut. Use only A or B (which one is up to you). The file must contain your circle name (at the top), give the viewer a brief idea of what you'll be selling, and be under 4MB. It cannot be nsfw (as in full out showing privates and titties) and the recommended format is png.

Next up there should be another page of guidelines, and then you choose your circle. (Stealing this pic from circle.ms' own jp guide)

Choose the circle you want to sign up as and click the orange button at the bottom of the page. Now the actual filling out starts.

I'd recommend writing your name in katakana both times, unless you have a name in kanji. When you're done, hit the orange button at the bottom of the page.

The next page will ask you to confirm the information. Hit the orange button if it looks good or the grey if you need to change something.
You will now need to pay the registration fee.

I'm choosing credit card payment. The page for that should be pretty self explanatory. Hit the button saying 次へ to continue.

Please note: I am using a foreign debit card, so you do not need a Japanese one.

Next hit the blue button at the bottom and it'll take you back to circle.ms.

Note that you cannot cancel your registration after the payment deadline has passed. Nor can you change the circle name or anything other than the address and phone number you entered earlier. Click the orange button to continue.

Red fields are required and yellow ones public. 

The questionaire is most likely different when one signs up for a latter comiket, so please use a translator to confirm the questions before answering.
Here's some some lists of occupations to use: one two.

Next they'll ask you about your sales results from last comiket. Leave blank if you didn't participate, and scroll down to the next one where they ask about what you'll be distributing at the upcoming comiket. 

After that there's a semi long questionaire about last time's comiket. Skip if you didn't go/don't know Japanese.

Then you upload your circle cut (The grey ファイル選択 button) at the very top. Note that your circle cut will automatically be made greyscale. Find the section that says "Webカタログ用サークルカット" to upload a version in full colour (for the web catalogue) afterwards.

After that, scroll to the bottom, click the orange button and you're done!

You should be seeing this when looking at the registration status:

Now.... Time to wait for the results.

To edit your info (if the deadline hasn't passed), go to the ｲﾍﾞﾝﾄ新規/申込中一覧 tab and scroll to the bottom until you see this.

On the next page you can edit each section by pressing the orange 更新 button.

This might be imperfect, but I hope it helps! Sorry but as a resident I'm not sure how to go about the address thing if you don't live here nor have a friend to help you. Maybe tenso or a similar proxy works, but I don't know. Don't take my word on it.

I'll update or make a part 2 when the results are out (if I get in, that is)

Wait, you need some special documents to sign up? you might ask.
Yes. When signing up for the next event you will need to enter two codes that can only be found in said set. There are three ways to acquire them.

1 & 2) Order the set online from circle.ms.
At the top of their site there should be a tab saying "通販・商品一覧".
At the time of writing, it looks like this:

If you order the physical set (which is cheaper), you'll get an A4-ish sized envelope in the mail from circle.ms, containing the sign-up pamphlet. The online set option is fairly new, so I have yet to try it myself. However, it says the comiket registration can be started directly after purchase, and the two codes will be shown at the order confirmed page. Also, the codes will be linked to your current account and cannot be transferred.

3) Buy the set at the previous comiket.
The comiket official booths in most halls should be selling them throughout the duration of the market.

I bought mine in advance from circle.ms, and it looks like this.

Inside you'll find an invoice containing the two codes necessary for registration.

Yes, I did both cover and mosaic my codes to be safe.
The set also contains everything needed for mail sign-up, but we'll be doing it online so just ignore all that.

Now then, head to circle.ms again and choose the "ｲﾍﾞﾝﾄ新規/申込中一覧" tab.
The next comiket at the time of writing is C97, so it looks like this, but it'll probably look different for C98 and later.

The first one is regular registration. The one below is for having two circles share one table (usually one space = half a table) and can only be done after both circles have finished the normal registration. I will not be covering this option in this guide.

next you'll end up at a page showing the event information, the rules and guidelines (run those through google translate to see) and the circle cut templates (A and B). Circle cuts are the images for each circle printed in the catalogue and on the online map. Important: leave the little square in the upper corner completely blank. Do not cover it or the side frames what so ever.

The one on the bottom is for the manga report and cannot be used as a circle cut. Use only A or B (which one is up to you). The file must contain your circle name (at the top), give the viewer a brief idea of what you'll be selling, and be under 4MB. It cannot be nsfw (as in full out showing privates and titties) and the recommended format is png.

Next up there should be another page of guidelines, and then you choose your circle. (Stealing this pic from circle.ms' own jp guide)

Choose the circle you want to sign up as and click the orange button at the bottom of the page. Now the actual filling out starts.

I'd recommend writing your name in katakana both times, unless you have a name in kanji. When you're done, hit the orange button at the bottom of the page.

The next page will ask you to confirm the information. Hit the orange button if it looks good or the grey if you need to change something.
You will now need to pay the registration fee.

I'm choosing credit card payment. The page for that should be pretty self explanatory. Hit the button saying 次へ to continue.

Please note: I am using a foreign debit card, so you do not need a Japanese one.

Next hit the blue button at the bottom and it'll take you back to circle.ms.

Note that you cannot cancel your registration after the payment deadline has passed. Nor can you change the circle name or anything other than the address and phone number you entered earlier. Click the orange button to continue.

Red fields are required and yellow ones public. 

The questionaire is most likely different when one signs up for a latter comiket, so please use a translator to confirm the questions before answering.
Here's some some lists of occupations to use: one two.

Next they'll ask you about your sales results from last comiket. Leave blank if you didn't participate, and scroll down to the next one where they ask about what you'll be distributing at the upcoming comiket. 

After that there's a semi long questionaire about last time's comiket. Skip if you didn't go/don't know Japanese.

Then you upload your circle cut (The grey ファイル選択 button) at the very top. Note that your circle cut will automatically be made greyscale. Find the section that says "Webカタログ用サークルカット" to upload a version in full colour (for the web catalogue) afterwards.

After that, scroll to the bottom, click the orange button and you're done!

You should be seeing this when looking at the registration status:

Now.... Time to wait for the results.

To edit your info (if the deadline hasn't passed), go to the ｲﾍﾞﾝﾄ新規/申込中一覧 tab and scroll to the bottom until you see this.

On the next page you can edit each section by pressing the orange 更新 button.

This might be imperfect, but I hope it helps! Sorry but as a resident I'm not sure how to go about the address thing if you don't live here nor have a friend to help you. Maybe tenso or a similar proxy works, but I don't know. Don't take my word on it.

I'll update or make a part 2 when the results are out (if I get in, that is)