First off, it really isn't wire, it's ribbon.
The tools required is a broken hack saw blade, an ability to draw smooth curves (some french curves available at a Office supply store are very handy), a fine toothed file, a wooden or metal rod, a soft #2 pencil, a good eraser and optional, some white wood glue.
The ribbon comes in Brass, German Silver and Sterling Silver. It's available from TOTW, Dixie and MBS. It usually comes in two thicknesses which of course can both be used on the same gun to add contrast and emphasis to the design.
Buy more than you think you'll need, it's cheap.
Take your time sketching the pattern. Erase what you don't like and redraw it. (I've been known to redraw these things many times before it finally looked good to me).
Break the hack saw blade off into pieces about 2 1/2-3 inches long. Grind the teeth off and the ends square (or slightly curved on the hammer end).
On the cutting end, grind back both sides about 1/4 inch along the length, leaving a central blade about 1/8 wide. It will look kinda like )_(
While your at it, make another one leaving about 1/4 inch for the central blade. (I also made one with a 1/16 inch blade but seldom use it except in the tightest curles). The 1/4 blade is good for long fairly straight areas.
Grind or stone the remaining blade tip so it is a sharp knife edge.
To prepare the ribbon, I like to trap the flat part of it between the corner or edge of the fine toothed file and a piece of wood or metal dowel. Then pull it thru this leaving little scribed lines down both sides. These will help trap the ribbon after it is installed.
To use the blade tools you've made put on your good glasses and position the blade on the drawn line. Use the metal or wood rod as a hammer and drive the blade straight down into the wood about 1/8 inch. (Of course, you can use a real hammer but go easy with it.) All cuts need to be perpenducular to the surface of the stock. (The depth needs to be a little deeper than the width of the ribbon).
Remove the tool and locate it on the line again so it overlaps the first piercing and pound it down in.
Keep going until the pattern is pierced.
I find it to be a good idea to go over the pattern twice to make sure there isn't an area down in the grooves that isn't connected. If this happens, the ribbon will not go into the groove freely and you will end up mashing the ribbon (and wood) when you insert it.
Place the ribbon at one end of a cut and use the metal or wood rod to start it into the groove.
Continue pushing the ribbon into the groove, bending it as needed as you go along to line up with the groove.
After an inch or so is started, I go back and, using the rod like a roller, push the ribbon deeper into the groove to hold it in place. Keep going until you get to the end of the groove, then work the ribbon down with the rod, rolling along, so it is flush (or almost flush) with the surface.
Some folks like to put a little white glue into the groove before installing the ribbon but that is up to you. IMO It does help anchor the ribbon.
After all of the ribbon is installed, wet the wood in the area. IMO, the wetter, the better.
This wetting causes the wood to relax and to return to it's original position. Of course, it cannot really return because the ribbon is in the way so the result is a very tight pinch on the sides of the ribbon. This is what keeps the ribbon in place.
The little grooves the file made on the sides of the ribbon just give the wood something rough to bite on which also keeps the ribbon from coming loose.
After the ribbon is installed, file it flush with the wood. If the ribbon is below the surface of the wood, sand the wood down flush with the ribbon but be careful. It is easy to create hollow or low areas in the wood adjacent to the wire and that looks somewhat frinkled.
On your first projects, keep it simple. Soon you will be getting into crossing shapes which requre precision cutting to avoid gaps. Often, these overlapping or crossing areas have the ends of the ribbon filed to a matching angle so there is no visable gap at all. This makes the ribbon seem to pass right thru another piece of ribbon.
You will also find that tight spirals are a real pain to do but they look nice when they are done right.
Another thing to remember. Because your will be driving the wire down into the wood, and this makes the wood want to move sideways, very small areas where the ribbon crosses another ribbon may chip out. IMO, it's best to keep crossings so they are not less than 45 degrees to the other ribbon, so now you have been forwarned.
I have seen some wire inlay which is so incredibly close to other wires it doesn't seem possible that the artist could do what he did without breaking or chipping the wood. I have no idea of how that is done.
Wire inlays add a lot to the looks of a gun and are much easier to do than actually carving in grooves and other fancy carvings.
Have fun!!