This is very possible, you just need to practice, and familiarize yourself with the process. The amount of money you can save by grooming on your own is quite impressive.
If you want just the basics, start with a clippers, a slicker, a comb and a nail trimmer. Also get some styptic powder incase you accidentally clip a nail too short.
Do some reading up on the subject, it's easy to find breed-specific grooming guides at a library or online. (The mix you have sounds like a nice one, I have a few Shih-tzu's myself and a close friend has poodles)
As some other people suggested, watching some videos on youtube or another video-hosting site is a good idea to familiarize yourself even further with the process.
A very important thing to remember is to not make this a traumatic or even stressful experience, for the dog or yourself. Always have a few treats handy to reward at the end of your session, and give plenty of reassurance if your dog seems to be stressing. Although, if your dog hasn't had a problem with groomers before, it shouldn't be hard for you to do it yourself. (My dogs are VERY temperamental when it comes to grooming time)
Grooming your own dog also lets you have a different degree of familiarity with how their body is as "usual" and you'll probably be quicker to pick up on any problems.
Have a fun grooming experience!
