At any given time, only about 3-4 SSBNs are out on patrol. The rest are in port or undergoing refits. Step one is to hit the ports, so you only have to worry about the 3-4 that are out. The subs patrol in defined patrol boxes which are roughly known to everyone.
Then you knock out the E-6s, E-4s, and all fixed VLF transmitters to remove VLF comms capability. Then you knock out, at minimum, the AEHF and Milstar satellites, but I've heard the SSBNs now can send up an Iridium buoy, which is good, that is a lot of satellites to take out. I don't know the feasibility of that. This buys some amount of time before a launch message can be received by the sub.
Now we would presume that before such a strike, the locations of the patrolling SSBNs are known. There are a number of new types of sensors such as green lasers, enhanced sonars, satellite wake detection, even antineutrino detection, about which some has come out in the open literature. There is also the emerging possibility of swarms of sonar equipped underwater drones that could aid in detection.
As for destroying the submarines, that could be any combination of attack submarines, underwater drones, aircraft with torpedoes, or aircraft with nuclear depth bombs.
It's also instructive to think about how a potential pause due to comms unavailability could affect deterrence as well, since an adversary could launch a first strike limited to military targets, and if the SSBNs were alive but out of communication, an adversary could threaten a follow up attack on cities if the remaining SSBNs did not surrender, and this would be an extremely difficult ultimatum to refuse.