If your concrete patio is good condition except for gray, splintering wood separator strips, repair is relatively inexpensive, and although somewhat time-consuming, fairly easy.
If you saw the patio when it was being poured, you may have noticed that there were nails driven into both sides of the wood strips to hold them down once the concrete dried.
You might assume that once you have removed the old wood and cut the nails from the concrete, there won't be anything to hold the new wood in place.
Not so. Once the wood strips have been removed there is a 90-percent chance that all the nails will have rotted away even if they were of high quality.
The wood strips, usually redwood, are actually held in place by the rough and irregular edges in the concrete that is, until the wood deteriorates to the point where there is no longer anything for the concrete to hold on to.
Replacement is rather easy. You'll need a hammer, a wood chisel and a hand saw, maybe a pair of side-cutters, a small vacuum and an electric sander or an electric planer or a small table saw (these can be rented) and a small block of soft scrapwood about 12 inches long.
First, use the hammer and chisel to remove the wood strips. No special technique is required. Just get the wood out as best you can. Be careful not to dull the chisel by driving the sharpened end into the concrete. You might consider using knee pads for comfort.
Once the wood is removed, use the side-cutters to shorten any nails that may remain in the concrete. Don't cut them completely away. Leave about one-quarter inch of the nail sticking out of the concrete. Again, if the wood is rotten enough to need replacement there probably will not be any nails in any case.
Next, vacuum the cavity where the wood was, being sure that no debris is left that will prevent a new piece of wood from seating properly.
Use the electric sander (or an electric planer or a small table saw) to mill the replacement pieces so that they are approximately one-sixteenth to three thirty-seconds of an inch wider than the average width of the cavity to be filled.
Cut the wood to length, and starting at one end begin driving the strip into place using a wood block between the strip and the hammer.
Simple physics holds it all in. As the wood is driven into the concrete cavity the sides of the strip adjacent to the concrete are torn upward. Between the compression created by installing a slightly oversized piece of wood and the upward angle of the torn sides of the wood you'll have a tight fit.
Clear, dry redwood must be used. Not just clear, but clear and dry. If green wood is used (green referring to moisture content, not color) it will shrink as it dries out and in very short order two to three months it will be loose and in need of replacement.
To make the wood last as long as possible, rub a couple of coats of clear wood preservative onto all six sides of every strip before driving them home.