Aidan, welding springs is nigh-on impossible to do and still keep the spring quality to the steel. It will break right next to the weld, due to the heat of the weld making the steel brittle.
It may be possible to weld, then heat treat the whole spring, and make it good, but given the time and expense required, and the probability of it still not being up to standard, you're better off buying a new one. They tend to be not very expensive.
If it's a coiled spring off something unusual, and you can't get a replacement, you might be as well off rivetting/bolting another piece of spring steel over the break. It'll still be a bodge though.
Garage doorspring? what I have done in this situation is to heat and make another bend at the end of the spring, on my doors this lasted several years before going twang again.