One of the first conventions players learn is the "Unusual Notrump." A jump to 2NT over the opponent's opening bid shows the 2 lowest unbid suits. A logical extension of this convention is to use Michaels Cuebids.
This popular convention works as follows:
Or, if you prefer it in words:
Usually, a Michaels bid is made with a preemptive (weakish hand, such as): K J 9 8 5K J 10 4 24 32. Over the opponent's 1-of-a-minor opening, I would bid 2-of their-minor with this hand (planning to accept whatever decision partner makes).
However, I could also make a Michaels bid with a super hand such as : A K Q 10 5A K J 10 4K 22. This time my plan is to put partner in game when he chooses a major.
There is a school of thought that a Michaels bid should be avoided with a medium hand such as: A Q 7 6 4A Q 10 7 65 42. The thinking is that when partner chooses a major, you won't know whether or not a game is in the picture. For that reason, many players choose to define Michaels as "weak/preemptive or very strong--not in-between." There are pros and cons to this philosophy; suffice to say that you should discuss with your partner whether or not he adheres to this practice.
What Suit Quality?
This depends a bit on your general preemptive philosophy. If you are an aggressive preemptor, your suit quality will obviously have the possibility to be worse than a sound preemptor's. I suggest that the vulnerability is the most important factor. Vulnerable against not, it wouldn't occur to me to commit a Michaels bid over 1 with, say: Q 9 8 7 5K J 8 4 24 36. At favorable vulnerability, I wouldn't mind a Michaels bid with those poorish suits. When Vulnerable, I like to have much better suits--better meat at the top. In all cases, 5-5 is the minimum distribution (although a former partner of mine would sometimes have 5-4...and I think I even recall 4-4). :)
After 1-2 or 1-2, the partner simply picks his best (longest) major and bids to the appropriate level. With equal length in the majors, choose the better one. If the partner of the Michaels bidder thinks there is a game, he can just jump there. (Sophisticated methods involve using 2NT as an ask). If the partner of the Michaels bidder is not interested in game, he should use the LAW of Total Tricks. Bid to the 3-level with 4-cards in a major (not an invitation), the 4-level with 5 cards.
After 1-2 or 1-2, the partner uses the same guidelines as above if he is "supporting" the major. If he has no interest in partner's major, he can bid notrump (on the appropriate level, again using the guidelines above) to ask partner to name his minor. Use care as responder; if you have only 2 in partner's major, and only 2 in one of the minors, don't get carried away (your partner's minor will usually match your 2-card minor--that is the story of life, as well as the bridge probabilities).
Just as with any convention, you need to make sure if it is on:
1) By a Passed Hand (I recommend YES)
2) In balancing seat (I recommend YES)
3) After opponents bid 1any--Pass--1NT (I recommend YES)
4) After the opponents bid and raise; for example 1-Pass-2 -- (I recommend you discuss this).
5) After Weak 2-bids; for example 2 3 (I recommend you discuss this).
Also, what if the opponents double your Michaels bid? What does partner's pass mean? His redouble? His preference?
For example: 1 2 Double Pass -- Does the pass mean he wants to play in diamonds? Does he want you to pick the major? All of this requires discussion.