Hey guys. So I'm not entirely used to playing two player, so this situation has me a little stumped. If I'm first player and declare my attacks, but leave a character who could legally attack ready, then play moves to the second player, does it come back around if I can still make legal attacks as the first player? Or do I only get one chance?

You only get one chance. Sequence is like this:
-First player does all of his defenses.

-Second player does all of his defenses.

-First player does all of his attacks.

-Second player does all of his attacks.

No extra chances to attack again. Was there a specific reason you left a character ready? Holding back a 'ranged' character that you ended up not needing, or some such?

I was trying to do something clever with Tactics Aragorn. I would've attacked with the second players characters, destroyed one enemy I left with Aragorn and then engage the other one and finish it off. Thanks for clearing it up though, I played it that way because I figured I was cheating.

You only get one chance. Sequence is like this:

-First player does all of his defenses.

-Second player does all of his defenses.

-First player does all of his attacks.

-Second player does all of his attacks.

No extra chances to attack again. Was there a specific reason you left a character ready? Holding back a 'ranged' character that you ended up not needing, or some such?

Just wanted to add that ranged characters can attack during the first player or second players attacks (but obviously only the once unless you can ready them after the first attack).

Question about ranged: if I have a ranged character as player 1, can I attack an enemy engaged with player 2 on my turn, then ready my guy and attack the same enemy again when player 2 has a turn? It says you can only initiate one attack per enemy, but you can participate in as many as you are able. So, if I initiate on my turn, can I participate in an attack initiated by player 2 against same enemy? If so, ranged characters can attack each enemy twice in a two player game, if able to ready.

Yes-- but player 2 does need to have a character ready and able to be exhausted for the attack. The ranged character is allowed to participate in attack declared by player 2. And the core set manual says the player needs to have a character ready to be exhausted in order to declare the attack: "In order to declare an attack, a player must exhaust at least 1 ready character"

GrandSpleen is correct. FAQ question 1.11 addresses the matter if you are looking for an official answer.

The thing about Ranged characters is, "it can participate in attacks that are declared by other players" (core set manual). It doesn't matter who they are engaged with-- SO, if you BOTH have ranged characters--

1- You declare an attack against enemy X using your Ranged character, and player 2 joins in with their Ranged character.

2- Ready both Ranged characters somehow.

3- Player 2 declares an attack against the same enemy X, and you can join in with your own Ranged character.

Doesn't matter whether he is engaged with you or player 2, that would work fine either way! 2 attacks against the same enemy.