Hi, Kendal, welcome!
I'm new to bonsai, and am just now getting my stock started...in other words, growing rather than trimming or overtly training. That said, one of the most important tools, in my opinion, is a really sharp knife. I use a small knife that I made from good iron, which can be sharpened quite easily. It fits in the hand well and has a sharply tapering, wedge-shaped blade that can get most places.

I also picked up a bonsai watering-can. This allows for good top-watering without disturbing the soil. I'm very impressed.

Josh

The one indispensable bonsai tool is called a concave cutter (8" is the norm). You can't get it at the hardware, so try a dedicated dealer (online could be www.evergreengardenworks.com, www.bonsaimonk.com, others... and you can 'fake' them with other tools and you almost don't need anything else (or can fake others) if you do have a pair. You should pay anything over $50.00 for some, though can get them cheaper, but a good pair will last forever (and can cost a lot more if you want). A knife is ok for certain little things, but you need a concave cutter for branches, etc.