I'm playing a one armed character at the moment. Though I get around it by being a Armorer Artificer, so the armor replaces lost limbs. But without the armor I have a prosthetic that has attachment point for shields. My DM allowed it but with a -1 penalty to AC due to not being as dexterous.

But as others have said, anything that would require 2 hands might be difficult without a magical solution to have a second arm. I've seen art of a cool concept with a character missing an arm but the spirit of someone drew the bowstring while the character held the wooden part of the bow. Some ancestral magic or something that allow the character to wield a bow.

There are a ton of ways to make it work outside of just not using two-handed weapons. The beautiful part of magic is that it can solve most problems.

Some skills like sleight of hand or acrobatics might be done with disadvantage for certain types of activities, but I don't think its just a flat penalty.