They require a wormhole drive to use, and cannot be used by rockets.
If you have an NPC crew then the fastest way to use a wormhole is to simply sit at the navigation console, select the wormhole and then set it as the waypoint. Your crew will then automatically fly to it and use it.
Alternatively it can be done by a player. To do this, he/she must sit in the Engineering seat and make sure all the 3 panels are centered then set the wormhole polarity (see below) and activate the Wormhole device, when your ship is ready the Commander of the ship must fly through the wormhole.
Polarity, from the manual: "Wormholes always exist in pairs, a positive wormhole and a negative wormhole. A positive wormhole is recognized by its blue and purple colors. A negative wormhole is slightly smaller than a positive wormhole and appears in red and yellow colors." You have to match the polarity on the engineer console to the polarity of the wormhole itself to use it safely. Using the opposite polarity when flying through a wormhole will destroy your ship.
Flying through a wormhole takes about 10-15 seconds.