If you get into doing any kind of bowl turning you might be interested in making one of these ...
http://aroundthewoods.com/oland.shtml
This is one of the most fabulous websites in existence for the new woodturner. Read every page of it and you will get more ideas, hints, projects and instructions than you will be able to complete in years. The first one to start with is the basic outline for a sharpening jig. I built my version of it years ago, with a 19.99 walmart grinder, and still use it today everytime I turn. total cost was about $25 for the grinder and some nuts and eyebolts at the hardware store.
I believe he has instructions for a pyramid tool or 120 degree point tool there somewhere, but I'm not sure that's where I saw it. If not, here's the readers digest version. Go to a pawn shop and pick up a few extra long drill bits between 1/4 and 1/2 inch. You want the ones that have a longer non fluted section. Use it or a new bit the same size to drill a hole into a handle blank the depth of the flutes + about an inch. If the fluted section is too long, you can snap off some, just leave about 2 inches of flutes + 1 inch of solid to epoxy into the handle. Turn the handle to fit your hand, and then epoxy in the drill bit with the flat, non fluted end out. Wrap a wet paper towel around the shaft about an inch back, and use some tape to secure it so it won't get into the grinder wheel. Get a cup of water and put it near the grinder. Dunk the tip from time to time to keep it from getting too hot, as you grind a flat on one side of the end about 1/3 of the total diameter. turn the handle 120 degrees and repeat twice. You can adjust the distance the tool butt is from the grinder wheel to change the angle till you get a sharp point with a flat edge about 1.5 times the diameter of the tool and all 3 angles as close as you can eyeball it to the same. This tool can be used to turn decorative grooves with the point, and you can use the angle edge almost like a skew to face or round the end of turnings. A very useful tool to have, and total cost is usually about a quarter for the used drill bit. If you get a drill bit that won't hold an edge, heat it with a torch till the epoxy turns loose, trash it and try another one. No great loss.
Another "usually" free tool is the dreaded butter knife parting tool. I say usually free, cause I know one guy that used one of his wife's good butter knives, and it cost him plenty! But any other butter knife will usually work, and actually a very old one from a junk store or "anteek maul" has a better chance of having better steel, so don't be afraid to risk 50 or 75 cents to pick up a few to try. Just set the butt down far enough from your grinding wheel to give yourself about a 45 degree angle on the first grind, and with the spine of the knife down "teeth up" grind the round tip to a sharp point. The arc you grind should be about 3/4 inch. Then turn over and relieve the point down about 1/4 inch, giving you a compound point somewhere in the vicinity of 70 or 80 degrees. Turn some scrap wood to a dowel, and part down into it about half way every half inch or so, about 5 or 6 times per knife. Discard the ones that get dull the quickest. I actually have an old carbon steel chef's knife that I ground the edge off of till the blade was a little over an inch wide, and did this too, so it's a little heavier, and it's my main parting tool, I use it more than my 3 or 4 purchased ones.