The important thing I have learned is to take the time to prep. Iron and starch your fabric before cutting. I starch my fabric very stiff. I cut the fabric in manageable sizes and then cut my block pieces. I don't try to cut a lot of layers at once if the pieces are small. When sewing block pieces be sure they match up perfectly, one side is not smaller the the other or crooked when laying together. Don't veer at the end of a seam.
I really like paper piecing the easy blocks. They are perfect every time. The software program Foundation Factory has all the basic blocks you can print out any size size for paper piecing. I like it better for paper piecing patterns then EQ7 (which is great) because the block patterns are all numbered and done for you. Try paper piecing the most simple of blocks and you won't get frustrated with blocks all different sizes.