If I had two Cs that were half notes right next to each other, and I wanted to hold the first one for two counts, then immediately play the second one after releasing the key for a fraction of a second, how would I notate that?
Depends on what instrument you're writing for. Since you selected 'piano' as one of your tags, I assume that's what you want to write for. There are a couple of ways to notate this. The way I'm most familiar with is to put a tenuto mark over each note (looks like a hyphen) and then a slur over that. (Or under and under, if the stems are up.) Be sure NOT to put a tie, but a slur. They look very similar but not identical.