What are some at home arm exercises I can do to be a better surfer? Preferrably no equipment needed other?

Push ups for sure, the better speed you have on your hop-up will make or break you when you drop in. Also, try wrist-weights and do some paddling (in the air). This will build your arm-muscles used for paddling in the water.

Grab some 1-gallon milk cartons and use those in-lieu of weights. You can do curls or dangle your arms strait down and use your fore-arms to pull them up to your arm-pitts.

Do pushups where you clap your hands at the top if you can. That will help the fast twitch muscles which will aid in getting to your feet easier. Next I would work on is cardio. The better shape you are in the easier surfing becomes. Trust me on this one. Pullups are ok but they don't work the same muscles you use in paddling. I use one of those excersize bands tied to the door, then lay on my bench (I have a workout room) and use that to give me resistance while going through paddling motions. If I were to pick one excersize to do, anything cardio would be my first choice, followed by the paddling, then the pushups. Popping up on your board is pretty much 50/50 strength and technique.

I would learn to mimic the precise way that an injured seal flounders around in the water. I would also practice surfing with 4-5 pound slabs of raw beef attached to each ankle. If this does not improve your surfing ability, lacerate your appedages until there is a steady flow of blood that pools around your surf board. These exercises may not make you a better surfer, but they will make you a better supper.

Avoid push ups ... they destroy your shoulders and elbows. Try filling gallon milk jugs with different amounts of sand and using them for curls or sliding a broom handle through them and use them for bench press.

pushups

dips

pull ups