The best way to learn if a company or a position is the right one for you is to test the waters with informational interviews or by donating your time through an unpaid internship. Informational interviews can be fairly easy to set up, and they can really tell you a lot about the company without the pressure of impressing someone for a job. You can arrange these interviews with companies you're interested in that may not necessarily have a current job opening. Ask questions about the company (remember the values you've identified) and about the jobs they have that might fit with your skill set. If you're lucky, one of these positions might open up soon, and then you'll already have a leg up on the competition by having a casual interview under your belt. Just be sure you don't try to take the opportunity to sell yourself for a job when you're supposed to be there to garner information about the company. It could irritate the person who's taking the time to meet with you and end up hurting you rather than helping you.
If you have the time and financial stability to offer your services free of charge, an unpaid internship with a company you're interested in is the best way to test the waters. An internship will allow you to get a feel for the team you would be working with and really investigate the company's culture firsthand. But remember, every day at an internship is like an interview. Even if they assign you the most mundane tasks, you should knock their socks off.