Unity specific - work on different scenes and different code files at all times, and merge in the other person's changes manually. If you both need to be working on the same scene, duplicate it and use the copy as a test. Otherwise, if you both modify the same scene, one person's changes will overwrite the other. You can still use source control for your source files, just don't move them around at all, in the file system or via Unity, once they're created.
Beginner advice - get yourself a decent diff/merge tool (I like WinMerge) and get used to using it to see what changes the other person made, and to manually merge changes in conflicted files. Set up a central documentation space, eg. a Google writing document or a wiki, and keep your documentation there - documentation should contain a basic feature list at a minimum so you know what you're aiming for, and ideally a task list derived from the feature list, along with a clear indication of who is working on the task. Talk to each other to get a rough idea of who needs to work on which task and cross them off the list as they get done. Keep revisiting and re-evaluating the list to see if everything is still valid and if you need to rework any priorities.