Sharing audio files across the internet has it's own limitations.
The best solution is to use something called Gobbler Collect which is a session in the cloud which supports Studio One Pro 2 and 3.
You can do it on your own, however some ISPs may limit or even block your bandwidth if they suspect you're uploading or downloading media content for nefarious reasons. Check with your ISP if there are any restrictions which may inhibit large media file transfers to and from a file sharing service.
You could use a file sharing service (DropBox, Google Drive, etc), but be careful, be sure to review any license agreements about who owns the content once you've put it in the cloud.
About uploading your sessions. Studio One is recording uncompressed 24 bit wav files, the files will be much larger than your average compressed MP4 or MP3 file. The size of your session folder will be quite large, hundreds or thousands of megabytes depending on the number of tracks, samples and plugins used.
Your project files are stored in your Documents folder (Mac or PC), open up Studio One, and then the Songs Folder. There you will find individual folders for each song you have saved. The entire contents of the song folder you want to collaborate on must be copied into the same directory of each of your others machines. You won't be able to store them online in a central place (on a web server somewhere) and write to that folder in real time. Using Gobbler will let you update changes, otherwise you'll need to copy and paste the entire folder to the other machine each time a change is made.
You will need to copy over the folders to each system when you want to view changes. Depending on the size of your session and your upload / download speeds this can take some time. Also make sure that if you have any 3rd party VSTs that one of you has purchased, that the other person has the exact same plug-ins, or when you load the songs, you'll get errors indicating it's looking for certain plug-ins.
If you're project is really large, sometimes just putting the entire thing on a thumb drive or a portable hard drive and mailing it might be faster (and possibly less expensive) in the end.