It's far easier to make a repair to steel pipe with copper than with galvanized pipe, because the galvanized calls for cutting threads on exact lengths of pipe. But first, call your local plumbing inspector or water utility and ask for a pipe recommendation. The water in some regions is highly corrosive to copper, making plastic (CPVC or PEX) a better choice.
Also be aware that directly joining two different types of metals, in this case, steel and copper, can cause rapid corrosion at the joint (called dielectric corrosion). To limit this problem, make the steel/copper connections with special dielectric unions rather than with a regular coupling. This type of union separates the two metals with a rubber washer and plastic sleeve so they don't actually touch each other.
To remove the old leaky joint, turn off the water at the main entry, drain the system and cut the pipe near the joint with a hacksaw. With a pipe wrench, remove the pipe back to the nearest joints, working in both directions. Check the joints to see if they're clogged or badly corroded as well. If so, consider continuing back until you find a clean, solid fitting. Unfortunately, one bad joint often means others or much of the system needs replacing too. Add a new galvanized steel pipe length (nipple) at each end and solder in your copper. Then take the union apart and solder the brass end to the copper and screw the steel end to the galvanized pipe. Finally, join the two ends with the large nut.