The Celtic knot is a very popular motif; we've been asked for it here at Woodcarving Workshops.tv several times. In these workshops I want to give you my approach to the carving of Celtic knots, rather than a particular project with the hope that you can adapt it to you own needs. It wouldn't take much to turn what we do here into a picture frame, for example.
You should recognise my 'approach' to relief carving from elsewhere on Woodcarving Workshops; it's simple, efficient and precise.
There are lots of Celtic strapwork or knot designs to be had online and elsewhere. Almost all the original ones you see are drawn in manuscript, carved in stone or created in metal. Wood hasn't survived but my guess was the Celtic knotwork was more likely either carved large in doors (perhaps something like the Scandinavian 'stave churches') or scratched in low relief on utilitarian items. Whatever, my point is that not all the designs you'll find online will suit woodcarving. You may have to redraw them (as I do here), and definitely try out on spare wood before committing to your special workpiece.
Book: The first (1951) to instruct on drawing Celtic knots. Still amazing.
Celtic Art - The Methods of Construction by George Bain