Once you know the rules of euchre, you'll find a few different schools of thought on what card to lead. Regardless of what you end up leading, the biggest consideration on your mind should always be the trump.
If you have three or more trump cards and some strong off-suit cards, it may be worth drawing trump to empty the table of trumps. Remember, there are only a maximum of seven trump cards, so if three are in your hand, that's at most four split among the rest of the table. Leading with trump means that a single drawn trump from each player clears all but one of those trump cards as obstacles for you.
It's worth leading the right bower here if you have it. Yes, you may theoretically be stepping on your partner's left bower, but you can't know for sure, and if you are long in trump, then it's a good idea to guarantee yourself this trick, but cheat and steal at euchre at your own risk.
Likewise, if your partner called trump, you can presume that a few trump cards reside in your partner's hand, and you may want to lead your lowest trump card. This will still empty opposing trump and hopefully allow your partner to take the trick and the lead.
As a corollary, it is almost always a bad idea to lead a trump suit that the opponent has called. If the opposing team has chosen a suit as trump, chances are that they have more of it than you, and you can't afford to hand them a free trick while wasting your few valuable trumps.
Most euchre strategies recommend that you lead with a singleton off-suit ace if you have one. A singleton ace is a strong lead for two reasons. First of all, if no other cards of that suit are in your hand, there is a higher probability that they are in your opponents' hands, preventing them from trumping your ace. Your best chance for an ace to make it around the table and win a trick is on the opening lead.
Secondly, after leading a singleton ace, you'll have a void in that suit. If someone else leads the same suit, you'll have the option of trumping or sloughing off, both of which can be powerful.
For the same reason, do not lead with an ace if you have more than one other card of the same suit. With only six cards in a suit, if three of them are in your hand, chances are good that one of your opponents will be void in that suit, and be able to trump your ace.
Pay special attention to the "next" suit, the same-color suit as trump. Since the left bower switches suits, this suit only has five cards, so even if you hold only an ace and one other card in that suit, leading with the ace will often be an invitation for your opponents to trump you. In this case, save your ace for later and hope it can win a trick once trump is all drawn out.
Null and Void
If you can't open a hand of euchre with a trump or singleton ace, you generally want to create a void for yourself, in order to open up the opportunity to trump in later. Leading a singleton card here, even though it's not an ace, is probably your best move. Getting a trash card out of your hand opens up the opportunity for you to possibly trump in later if the suit is led a second time.
Leading a non-ace non-trump card is also a clear signal to your partner that you are creating a void for yourself. This is a fact your partner can use to their advantage, leading you back to the same suit later in the hand to allow you to trump in. Conversely, if your partner is void in the suit you lead, it is obvious your low card will not carry the round so your partner can trump in to take the first trick.