Bidding a high point Bridge hand
Typically, with any strong hand (something like 17+) you should begin with a takeout double (if it's available &mdash; see below). In this case, your hand is even stronger than that, so you should probably cue bid hearts after almost any bid by partner:


after 3S, 4C, or 4D, you have enough to insist on game with very little from partner, so cue bid 4H to force to game.
after a jump to a suit game (4S, 5C, or 5D), partner is showing something like 10+, so you almost certainly have slam and may have a grand. After 4S, you can bid 4NT to start asking about partner's kings. After 5C or 5D, you can cue bid 5H to force a slam and start exploring for grand.
after 3NT, you might just bid 7NT, as it's likely that you have 13 top tricks and it's difficult to imagine having a good constructive auction without strong agreements with partner.


Update:
TimLymington points out in the comments that you may have agreed that double here is for penalty. I had not considered this, as I play in the U.S., where the overwhelming majority of pairs play doubles as takeout at least through 4D and often higher.

If double would be for penalty, I recommend doubling and continuing as above except at unfavorable vulnerability. Game for your side is almost certain and slam is a possibility, but it seems difficult to explore for slam when X is not takeout. I expect to beat the opponents by 3 tricks (they'll likely get 6 trump tricks and nothing else), so I'm happy defending when at favorable or equal vulnerability, but the 500 we'll get at unfavorable doesn't compensate us for the 600+ we expect from making our own contract.

In that case, I recommend bidding 3NT, which is a small gamble, but requires very little from partner (the club K guarantees the contract, as does the diamond ten with the spade K, for example).