This is a bid of the opponent's suit, it traditionally shows 5+ in both majors if they are unbid. If one of the majors are bid, Michaels shows 5+ in the unbid major and 5+ in one of the minors. As you can see, Michaels first and foremost focuses on the major suit(s). Some people play specific Michaels (the minor suit is specified) whereas some people play that it could be either minor. Lets explore that all and begin with some examples
What it is?
Lets use some examples to illustrate that.
Example 1
Here South has bid the opponents suit - this triggers "Michaels Cue Bid". Since neither of the majors have been bid yet, it shows 5+ in both majors - a perfect bid for South's actual hand.
Example 2
Here we have cue bid the opponents suit again - triggering Michaels. Of course we are not showing hearts, since East has already shown 5+ hearts. This time we are showing 5+ spades (Michaels always shows the major(s) that haven't been bid yet), and 5+ of either minor. The exact minor is unknown to both opponents and partner at this point.
What about when two bids have been made? (Careful - agree this with partner)
Example 3
It is quite common to still be able to Michaels here, but to trigger it, we must bid opener's suit, not responders. (Many partnerships play that a bid of responder's suit in such a situation is in fact natural!). It is worth flagging this with your partner, give the auction and ask - what is 2♣ here, and what would 2♥ have been instead?
How strong do you need to be?
This is a point of contention, not everyone agrees on this. My suggestion is to just keep it simple and play it as 8+ points. If your style is to be aggressive when NV, you can drop that to perhaps 6+ points. But let common sense prevail, if you Michaels and have 20 points, don't just pass partner's response, bid again to show extra strength.
An alternative style is to EITHER be weak (say 9 points or less) or strong (16+ points). That way, partner knows if you bid again you have that strong range, and otherwise you are weak. But, that means with the middle range (which occurs frequently), you have to simply just overcall your suits slowly and naturally, and can't roll out a single bid to show your hand. This is a matter of style - you gain a bit more accuracy with the high card point message you send, but you lose a bit of flexibility and frequency of using a useful bid.
Responses to Michaels
So, partner Michaels, what should you do?
Raising Partner
Common mistake: When you have a major fit, you should show it with some emphasis, don't simply bid 2♠ (which could be done on a misfit), bid 3♠ to say - I have a real raise, a respectable hand with 3 trumps.
Lets change your hand a bit, where you no longer have a spade fit
Pass or correct
3♣ is pass or correct - telling partner that you want to play in his minor, so to either pass 3♣ or bid 3♦ if that is the long minor. A good rule that avoids any confusion is
Rule: When the Michaels bidder could have either minor, a bid of 3♣ or 4♣ are both pass or correct. What about the 5 level? Use 4NT as the Pass or correct trigger for the 5 level.
Strong response
The standard strong response is 2NT, so, for example
Here you are letting partner know that you are invitational or better. It is normal now for partner to reveal their minor - and you can now raise it again to show further strength.
Common mistakes
#1 - The most common mistake that I consider to be a significant error is using Michaels with the wrong shape, 5/4 shape specifically. It should show a minimum of 5 cards in either suit. Having 5-4 shape is significantly different - I strongly recommend being disciplined with this bid and not using it unless you have 5-5 shape at least. 6-5 shape is fine as well.
Another common mistake is getting confused with pass and correct bids. The rule of 3♣ and 4♣ are always pass and correct are good ones to set in stone.
Another common issue I see is people not doing enough with 3 card major fits. They simply bid the major at the lowest level and the Michaels bidder will be discouraged they are misfitting, and not do more with a good hand (that is discussed above in responses to Michaels).
Advantages of using it
Michaels is very popular and has the distinct advantage of conveying a lot of information in a single bid, so you can quickly find trump fits. Consider this auction where you do not play Michaels
In this auction you simply bid 1♠ because you aren't playing Michaels. The bidding comes back around to you - should you try 4♥? If you don't have a fit you could be in a lot of trouble, it is a gamble. If you had shown both majors on your first bid, you would comfortably pass - as partner has all the info needed to make a decision over 4♦.
Disadvantage of using it
The main disadvantage of using it is when the opponents end up declaring - they will almost know your exact shape early on in the hand. Against an expert declarer that can be a very costly concession.
Recommendation
I recommend using Michaels, it is fun and enjoyable as well as effective. It gets you in the bidding more and helps you reach big fits quickly - the primary goal of bidding! The biggest issue is lack of partnership discussion around it, knowing when it does and doesn't apply. It is worth trying to have a chat with your partner about it as always when adding conventions.
Read next: Second Suit in Competition: Compete with Purpose · Lebensohl Convention Explained · Preempting in First Seat: When to Be Bold · Preemptive Raises: Why Big Trump Fits Beat Big Points