With online applications, you create an ImmiAccount, start a new application for the applicant (Click "New Application" and then "Migration to Australia by a Partner (300,309/100,820/801)"), answer a ton of questions, hit "submit", pay (or maybe pay and then submit, can't quite recall), get a TRN number, then get taken to a page that gives you a list of documents to upload. It looks like this after you've started uploading things:
Attachments
Keep in mind that that checklist of documents is definitely NOT exhaustive - it doesn't include everything you'll need to provide, and it DOES include things that might not apply to you. It also includes the 40SP, which is not necessary as long as you're going to complete the sponsor's application as well (I'll get to that in a second). The checklist is not specific to the applicant. If you have a piece of evidence that doesn't fit any of the listed items, click "Attach Documents" in the top right corner - many more categories of evidence there.
Two things to keep in mind in regards to the attachments you upload: 1) Maximum file size for attachments is 5 MB; and 2) It seems there's a newly-implemented system restriction that only allows you to upload a maximum of 60 files per application (so total of 120 when you count sponsor's application and applicant's application). So keep that in mind, and try really hard to group evidence together in single documents - all your financial evidence in one PDF document, for example. When I personally scanned our files, I did not use the maximum quality setting on the scanner (to reduce file size) and I used the scanner's software that allowed me to scan multiple pages into a single PDF document. Then I used compress.smallpdf.com, which is free, to compress those files further. There are multiple programs available that can both merge and reduce the size of PDF documents, so if one doesn't work for you, you can try another. Obviously use caution and care whenever you're downloading any programs from the internet.
In this section you're uploading documents specific to the applicant, as well as all your other evidence if you like. I'd reserve any documents/evidence specific to the sponsor for the sponsor's application, though (I'll get to that in a second).
It doesn't TRULY matter where you upload your evidence (applicant's application evidence section or sponsor's application evidence section) - as long as it is attached either place, the CO will look at it, and it will be counted.

So decide what makes sense to you. Like I said, I uploaded the majority of our evidence on the applicant's part, and saved my husband's ID documents for the sponsor's.
Once you're done uploading to the applicant's section, you're just done with the applicant's application - there's no additional "submit" button when you're finished with it or anything.
At any point AFTER you hit the submit button & pay for the applicant's application and get that TRN number, you can start the sponsor's application. Go back to the homepage of your ImmiAccount (where it says "Summary of Applications"), and click "New Application" and select "Sponsorship for a Partner to Migrate to Australia (300,309/100,820/801)." At some point it will ask for the TRN - this is the one you just got from the applicant's application. Then when you're done answering the questions, it will again take you to a checklist of documents to upload - again, you can upload documents specific to the sponsor and whatever other documents here that make sense to you to have here.
In both applications, during all the questions you're answering, there will be a serious of five text boxes where you enter text about your relationship - finances, social context of the relationship, history of the relationship, etc. etc. Each one of you needs to write these in your own words. If you don't have enough space, you can also write your statements separately and upload them, and just write "see uploaded document called ___.pdf" in each of these boxes. If you do decide to just put your comments into those boxes instead of a separate document, just note the character limit before you begin. There can be formatting issues if you decide to write it in MSWord and then copy and paste it over, so I suggest just writing it in a plain text editor like Notepad instead if you're going to do that. If you're getting an error about special characters, try taking out apostrophes and dashes - that usually solves the problem.
Once you're done uploading things to the sponsor's application, you're done. There's no fanfare, though it feels like there should be.
Try to get everything uploaded within two weeks. Why? Here's MARA-registered agent Mark Northam's explanation:
http://www.australiaforum.com/739722-post5950.html
By the way, the online checklist says evidence of health insurance is required for Partner Visa applications - it is listed there incorrectly. It is NOT required.
Hope that overview helps!