1911 grips are about as simple as it comes. And another method would be using simple handtools for the whole job.
There's nothing at all wrong with the use of the power tools that houseofzeus used but you can do something this small without power tools and it'll take hardly any more time at all. In fact even though I've got lots of power tools I'd only do the initial cutting of the blanks with a saw, drill and counterbore the screw holes in my drill press and then all the rest would be done with basic hand tools.
If all you have for tools is handsaws and hand drills that's fine too. It simply means you'll need to make up a depth limit sleeve from some sort of tubing to control how deeply your counter bore drill hole cuts into the grip blank. And regular hand saws and sandpaper along with a bit of care and attention will more than adequitely fill in for some sort of power saw.
Keep in mind too that if this is your first time at this sort of thing you do NOT need to start with some fancy %50 burl blanks. It's very permissable to start with a scrap of hardwood flooring or a scrap of some other less than exotic wood. I would suggest though that it be a hardwood like maple, walnut, birch, oak, cocabolo or some other HYARD wood. If you can easily make a noticable depression in the surface with a fingernail move on and find a wood which leaves nothing more than a shiney line from your fingernail pressing.
With the basic outlines done use a round file to cut away the corners for access to the mainspring housing pin and mag release buttons.
A neat trick for this is to attach the grip blanks to an 18 inch long piece of 2x2 using the screw holes you accurately drilled and counter bored as "step two". Then with new coarse cut metal files kept strictly for wood working you thin and arch the shapes. Using the big files gives you a lot of control over the shaping. Just stop and check your progress as you go. I can't see each side taking more than 5 to 7 minutes worth of roughing unless you're very new to wood working. And if it does take you longer that's fine too. It's easy to take more off but a lot harder to put it back on. Just aim for achieving the right smooth arched shape right to the center line.
During this roughing phase it's very easy to demount the grips and install them on the gun to try the fit out. Be fussy, you'll be shooting them a long time.
Once they feel good but just a little fat when roughed out remount them on the holding stick and sand them smooth using a series of progressively finer sandpapers.
If you're after a stippled finish once you get the sanding done mark off the panel shapes for the limit of the stippling. Ideally you'd carve a shallow and smooth demarcation groove along these lines with a sharp knife for a crisp look to the work. From there get a very small ball end cutter for a Dremel and start randomly stippling the friction areas. Some practice on a bit of scrap to get a feel for it and develop a style to the look is HIGHLY recomended. We seldom get this sort of new skill right first time around. So take your time and work on the "look" to your stipple pattern. Be sure to use a light touch and clean the cutter often to prevent friction burning the stipple pattern.
Once done flood on a good finishing oil, let soak in for 5 minutes and buff off. Repeat with a few more coats with about a week between coats or according to the supplied instructions. Depending on the oil finish 3 to 4 coats and it'll have a nice looking buff but deep finish you'll be proud of.