There are a lot of different names and some of them describe the same exercise. Example, I learned a move called French Press which I found out later is also known as a Skull Crusher. www.youtube.com/watch?v=HgCRn2Rdoxc
Mountain climbers are straight forward www.youtube.com/watch?v=DyeZM-_VnRc
Lat raises ? Could be called side laterals. www.sparkpeople.com/resource/exercises.asp
Russian twist www.youtube.com/watch?v=4DYuSXvpu0g
If you're new to strength training, you might want to start with the Spark Fitness section. Coach Nicole has a bunch of short 10-15 minute strength workouts that will teach you some basics. Otherwise, I highly recommend that you buy or borrow these two books.
New Rules of Lifting for Women - Cosgrove
Body For Life - Bill Phillips.
Both are good beginner strength training books that will teach you the basics.