1) Any three Trump are worth bidding. Even if you have the three lowest Trump are three suited and have no Aces or Jacks. You won't stop anything with a hand like that. If you pass your opponent will either call it and likely make their point, as you can't help your partner euchre them. Conversely, your partner can call it and their likelihood of getting euchred is higher, as you can't help them in making their point. Remember, that with 3 trump, there are only four trump left between your opponents, your partner and the kitty. You can always get a great surprise on a hand like this. Your partner could have the right, two trump or help with aces. I have also seen 2-3 trump buried in the kitty before.
2) Be careful when ordering up trump to your opponent . Whenever you order trump you are likely putting a second trump in their hand. Not only that, you are allowing them to void a suit. Even that low trump you gave them will frequently take a trick. Even with three Trump be careful!
3) Never order the right bower to your opponent. Remember it will likely be their second trump, plus you let them void a suit. Most people won't pass on the right bower anyway unless they are extremely conservative, which will give you a chance for a euchre. If you have four trump or left-ace-king, you should order it up though.
4) Always pick up the right bower unless you have a complete junk hand. Even one other Trump is enough to call on.
5) order up your partner with a lighter than normal hand. You are given them hopefully a second trump and allowing them to void a suit. Remember that the dealer position is the best at the table.
5) don't call four suited
6) don't call on two trump unless one is the right or you have two offsuit aces.
7) Do not be afraid to get euchered. All good players get euchered. If you don't call it your opponent will likely call it and make their point. Getting euchred really only costs you one point.