starting to lift weights

Hey!

I would like to introduce some weight lifting into my workouts. I am not very strong, and struggle to do pushups. Kind of embarrassing for me so I want to build strength and also tone my arms.

Are there some basic exercises I should start with? I would rather use free weights than the machines, because they intimidate me!

Some friends told me that if I start doing curls or something and do it wrong I can hurt myself. I'm not sure if they were being dramatic or not, since I'm not going to be starting off with a lot of weight. But, I don't want to form bad habits/bad form.

Also, I go to my gym on campus (I'm a grad student) and they don't have trainers or anything like that, otherwise I would get help from a professional. I know that is something a lot of people recommend.