Most shower arms have a bend in them. Assuming that it isn't a really cheap arm (flimsy), that angle should give you enough leverage to tighten it up without tools. You will need either pipe dope and/or teflon tape to seal the threads to prevent leaks at the fitting, though. One or the other should suffice, but I see a lot of plumbers using both - can't hurt. A shower arm doesn't have a bunch of water pressure in it unless it has an on-off valve in it.
More tape is not better. Two turns is enough. You want it snug (from just screwing it in), then probably another 1/2 turn (using the force available from the angle). More is okay if you need to get the angle aligned. Check it, and give it more if needed. You don't want it moving around if you adjust the showerhead.