How many weapon schematics are there in Fallout New Vegas?

Fallout New Vegas doesn't really have a whole lot of weapon crafting, unless you're into Explosives and want to make bombs. In fact, without DLC, there's exactly one craftable weapon that isn't a bomb or mine - the Dog Tag Fist, which you can make with a Repair skill of 30. The schematic can be had from Private Halford at Camp Guardian.

If you have Dead Money, you can do a few upgrades to the Cosmic Knife, turning it into the Cosmic Knife Clean or it's Super Heated variant, or a Knife Spear, which also has a Clean version. You'll need the Repair skill to make these, with 50 being the highest number required, but you don't need any special schematic.

With Old World Blues installed, the only craftable gun in the game becomes available, FIDO is little more than an upgrade to the K-9000 Cyberdog Gun, and is one of the only two weapons for which you'll need a schematic. It's found in the kennel at the X-8 Research center. You'll also need a Guns skill of 75

Finally, Lonesome Road adds the Fist of Rawr. You'll get the schematic automatically when picking up the component parts after killing Rawr, and crafting this powerful fist weapon requires an Unarmed skill of 75.

As for bombs - very few need schematics. Most just need a high Explosives skill, and, in many cases, the Mad Bomber perk and the Gun Runner's Arsenal DLC. You can view the full list of craftable items here. In general, crafting in NV is much more geared towards chems, healing items, food, ammunition, and other consumables than it was in FO3. There are few, if any craftable 'durable goods' of any worth.