Just play the game a lot and you'll learn when to bid and when not to. I find euchre to have a fairly small amount of strategy to it.
In general If you have 3 trump and one of them is A or better, then you can feel free to bid. If you have some off-trump Aces, than that's a good sign and you should bid.
You also have to consider what card you might be giving to the dealer, you don't want to be giving an opponent the right unless you believe that you will win 3 out of the 4 other tricks.
Going alone is all about game control. When deciding about whether or not to go alone, You have to consider how much control that you'll have over the game, and you have to consider what can take your control away.
for instance, if you get to go first and you have
right Ace King of trump and two off-aces, than you can try to draw the left out with your right, and if you do, than nothing can stop you from winning all the tricks.