If you are not going to graduate school, you will not (in most cases) be a computer scientist. In the same way that many doctors who finish medical school and do not engage in research are not necessarily scientists.
The most important thing is practical experience. Internships are invaluable.
The second most important thing is to get up to speed on real world coding practices. These are the things not taught in school, since a well-written program has no benefit in grading most courses. Depending on the language you like, read things like Effective Java, Code Clean, Code Complete, etc.
The third thing is to try and get used to reading existing code. Find some existing program, like an open source game, IM client, or anything. Try to dive in and make some changes whose effect you can observe. If you can learn to read code and join existing systems rather than write from scratch, you are better off than 90% of your peers.
Fourth thing is to figure out if you do want to be a computer scientist rather than an engineer, and whether you want to go to grad school. Read everything on SO about PhDs before you take the leap.