When doing an inlay such as what Gene mentions, the use of a template and router to create the pocket and the inlay is by far and a way the best and easiest way to go about it. Fit is wham bam spot on. Seldom is there much in the way of having to tweak anything. Setting the bit to the correct depth to cut the pocket is probably the most difficult part of the process. Taking into consideration the glue, I try to set up to where the inlay is just flush or only slightly proud. Too proud and you run the risk of sanding thru the inlay, too shallow and you end up sanding way more than what you might like.
Depending on the type(s) of wood used for the inlay and multiple changes in grain direction a well turned card scraper, carefully used does a great job. Otherwise, a ROS is the ticket. Some woods tend to bleed over into others. Redheart and American Holly come to mind...Even with a ROS I still get bleed over. red into the white. But with a card scraper, not so much..
When doing freehand inlay, the use of a router is IMHO still the way to go for clearing out the pocket. The pocket doesn't have to be dead nuts flat, just reasonably close. Again, its more a question of depth control. Various thickness's in veneer's has to be calculated. Not all veneers are cut equally. Most raw veneers range anywhere from around .025 to .040 +/-. then there's paper back, wood backed, blah, blah, blah.. you get it..... The Veritas router plane (shown above) excels at what it is designed for. It works as well as it looks
When it comes to use in inlay work, clearing out a pocket from scratch is a bit of a PIA. The harder the wood, the bigger the pain!!! Not impossible in anyway, just better, easier and quicker ways to go about it. Works well cleaning up the edges as long as the base stays on the outside edges. I've found using a sharp chisel/scapel is every bit as quick. Putting a proper edge on the router plane bits can be a bit challenging as well.
The inlay cutter head option is hard to beat when it comes to banding and straight line string work. Clean, neat and repeatable when using a fence. Depth and width control is extremely adjustable up to a point and works with most commercially available string or banding. Free-handing anything with a curve or radius is another story altogether. On softer woods, it works pretty well. Only because you can get the depth correct usually on the first pass. Heavily grained woods and hard woods require a steady hand. And usually the best route to take is multiple incremental passes. For me, the use of a magnifying glass and a sloooooooooooooooooow pull is what it takes. When designing string work, take into account your radius's and grain direction. Work with the grain and keep your curves shallow enough to get a router plane bit in the groove to clean it out. This is determined by the length of the heel of the bit. Otherwise..a very very narrow or micro chisel will be need to clean out the groove. Alot of work, and a lot of room for the dreaded OPS!! know wut I mean!!!!! Done well, it looks great.
Having gone on about all that, recently I've been experimenting with micro router bits for string work....very promising results thus far. I found bits down to 1/64" in 1/8" shafts on ebay. Work nicely, but tend to leave fuzzies and I've broken more than a couple so far by not taking my time. Lee Valley has mini downcut spiral bits that i'm gonna give a go. Supposedly leave a nice clean edge. At around 18 buck a bit, not inexpensive...