After the spokes and rim have been thoroughly cleaned, start to lace the wheel. On your vintage wheel, in most cases, you will see some slight wear marks from where the spokes were originally. this will help you place the outside spokes where they were prior to cleaning. String all of the outside spokes, then all of the inside spokes on one side of the hub first. Place the rim over the top and begin to thread a few of the nipples through the rim onto the spokes. Flip over the wheel and do the same to the other side. You will have to loosen and tighten spokes in order to get all of the spokes strung evenly. After all of the nipples are threaded hand tight, try to evenly tighten the spokes with a wrench. Test the spokes by tapping them with a wrench as they all should produce about the same tone if they are under the same tension. This part takes a while. After you've finished up, bring it to a local shop for truing and a once over.
The tires that will be mounted on the rims are some Michelin Gazelle M62's. 18" x 2.75" front and rear will cost you about $24 a piece.
Typical oxidized finish followed by Atypical mirror finish: