Pro Tip - ALWAYS use a clamp with wings, it will save you so much hassle.
Have you ever tried clamping the tooth, then putting the dam on the frame FIRST, then putting it on the tooth? One of my endo instructors showed me that when I asked the same question you are.
I only use dams for Endo, so single tooth isolation, but I usually always put it on myself with possibly minor help from an assistant if I have a regular frame. Don't worry, once you get out you can get much better dams - the one I use has the frame built into it and is awesome.
I almost always use 14A clamps, they're pretty aggressive but they hold on tight even if the crown is short. If the crowns are short and the dam keeps sliding off the other teeth, put as many teeth through as you can, then while one hand is holding down the dam, use the air syringe to dry the teeth and they'll hold in place better. You can also use split dam if your instructor allows it.