I'm so pleased you have a pair of Alexes! They're beautiful birds and quite intelligent too!
You really need to put a stop to the biting behaviour because those big beaks can inflict some pretty serious damage. My boy, Barney, bit my index finger to the bone on the day I brought him home. Thankfully, he's never done that again, but I'll always remember that special pain. I make sure I don't irritate my birds to the point where they feel the need to bite me.
You say you haven't had pets before, so that indicates you need to learn to watch your birds carefully. When an Alexandrine is angry, it will flatten the feathers to its head and body and 'pin' its eyes down to tiny pinpoints with white rings. It might or might not open the beak slightly to warn you of a bite coming. If you offer your hand and ask it to 'step up', watch what the bird does. If he steps willingly onto your hand, that's great. If he sidles away from you and tries to avoid stepping up, DO NOT force it. You'll need to go back and retrain the step up command so the bird does it willingly and without the need to defend itself by biting.
The first thing you need to do is work out *why* your birds bite. Is it because they're afraid of you? Are they afraid of each other? Is your house noisy with a lot going on (that can induce fear in a young or newly-moved-in bird)? Or, are they biting out of greed or competing with each other for food? Maybe they've just begun biting and now it's become a habit they do for no reason. Whatever, you need to figure out what the cause is. Then, we can work on ways to train it out of your birds' behaviour.
It would be useful if you could let us know some more info about your Alexes. How did they come your way? Were they abused in the past? Or, perhaps, misunderstood and punished or treated badly? Have they had any training at all (eg. 'step up' or target training)? What are they eating and are they receiving enough food? LOL! Sometimes, we old members tend to write novels at poor newbies who just came to ask a question or two, so please let us know exactly where you need the help and we'll try to keep it brief.
I'm certainly not an expert, but my Beaks came from a sort of neglectful home, where they were housed with a large collection of other parrots and lived in a noisy rambunctious environment. They were very nervous at first but with help from my friends here I managed to reach an understanding with them. All it takes is a calm approach where you break the problems down into easy pieces. Do feel free to ask questions: we're all here to help!
PS. Useful hints:
1. Always carry a chopstick when you have your birds out. If necessary, you can offer that for them to bite instead of your hand.
2. Don't seize an Alexandrine by the body or pet it on the back or head. Many of them *really* don't like it!
3. When you offer your hand, offer the back of your tightly-squeezed fist. Birds find it hard to bite that, so you can avoid a really painful nip.