When the bidding proceeds 1 minor - 1overcall - double - 2, opener needs a method of distinguishing between bids that are competitive, invitational or really strong. There are two different approach's to solve this problem
Using the good bad 2NT method, all openers rebids at the three level are invitational, showing approximately 15-17 HCP. With a hand that merely wants to compete because of distribution, you bid 2NT artificially. Responder usually bids 3 (if he can stand to play there), opener may then pass or rebid 3 or 3 non invitational. Since 2NT is forcing, it can also be used on very strong hands, in which case openers third bid will be 3 or higher. Double of 2 by opener can be used to show a strong balanced hand (good 17 to 19) , responder can convert the double to penalty if flat.
In this method, openers direct 3 level rebids are competitive only, they show sound values but insufficient to invite. With invitational or better strength opener bids 2nt and then continues over the semi-forced 3 rebid. As with good-bad 2NT, a bid of 3 spades or higher by opener on his third turn shows a very strong hand (9+ tricks or 18+ HCP). A double of 2 would show a balanced hand in the strength above your 1NT opening. It is probably best to specify that the bid either denies or promises a spade stopper.
A variation on weak must speak uses 2NT as a natural bid, and double for takeout with some invitational or better hand.
Note that weak must speak is not a licence to bid on garbage, opener should not compete with 3 on a 12-14 HCP that has potentially wasted values in spades, he needs 13 HCP outside of spades to bid 3.
Comparison of the two methods
The good-bad 2NT is very similar to Lebensohl, hence intuitive to those familiar with that convention. My own preference is for the weak must speak method since it allows opener to make a descriptive, lead directing bid immediately. The good-bad 2NT method may get shut out completely if the overcaller rebids 3 or 4 However the most important thing is to have some kind of agreement. It is possible to extend the agreement to the auction 1-1-D-2, and even to 1x-1-2 bid - 2 as well. Thus whatever method you use can apply to any auction where the opponents have a fit and the bidding is below 2NT.