The smallest chainring on a crankset generally isn't going to have much in the way of shaped teeth or shifting aids. Those are necessary to lift a chain from a lower chainring and since there isn't a lower chainring than the inner, those aids simply aren't needed on the inner ring. If you see "splits" on that small chainring, there's a decent chance they're damage and not there by design. (I'm speaking in generalities, but it really would be nice to see a decent pic to confirm.)

If the crankset needs replacing, a replacement crankset is easy to find. Eyeballing the crankset, I'm guessing it's a 28/38/48 triple. (Since the picture's taken from the non-drive side, I'm not 100% sure on that, so you'll need to count teeth to be certain.) And if the bike's the same size as the one pictured, the crank arms are probably 170 mm in length. Inexpensive replacement options would include Shimano FC-M311 or FC-M171 cranksets, which can be found online for about $20. Both of those cranksets are designed to use a 122.5 mm bottom bracket, so add a Shimano UN-55 bottom bracket in that length for another $20 or so.

If you don't have the tools to replace square taper cranks and Shimano splined bottom brackets, you may need to buy a couple of tools as well. A Park Tool CWP-7 crank puller will cost you $15-20. A Park Tool BBT-32 bottom bracket tool will set you back about $15.