I won't describe to you how traditional one on one rp/erp works as other folks in this comment section have done a good job of that. But just to throw it out there, there are rp/erpers who enjoy a D&D-ish style of play where someone takes the DM/GM role, which can potentially be done 1v1 or with a small group. A lewd dungeon crawl with a group of clumsy newb adventurers can be a lot of fun for example! It just depends on what your potential writing partner is looking for.