If you're lucky, find a group of racers that are around you and start racing with them. That's really the best way to get your feet wet. You don't want to jump into a big national event right out of the gate, it can be pretty overwhelming. Also, since you're running nitro, you'll need to either find other nitro guys, or find guys that are willing to let you run with them. Most groups/events have at least one "run what you brung class" at the very least.
Also, try to find people that race "dry tire". For starters, that gives your nitro a car a fighting chance. If they are using tire preps (which IMO is not really "no prep" but that's a whole other conversation), then most nitro cars have very little chance. If you can get your car to run in the mid 2s range, say 2.4-2.7 on dry tire, you'll be fairly competitive. Don't listen to the guys saying they ran 1.6 or 1.7 on dry tire - that's BS - they're using these new "rubs" on their tires which is NOT dry tire, but some groups allow it for some stupid reason.
As for getting faster, well that's easy. Get rid of
weight. Add
power. Add
traction.
For
traction, your rear tires need to be belted, or use tire bands - otherwise they will balloon, and you'll wipe out on the top end. Use something to condition the tire - my go-to is WD-40. Wipe the tire clean with it, let it sit for five minutes, and the tire becomes tacky. At the staging line, use a carpet (wool if possible) to do a pretty decently long burnout to heat the tires up. Very important in dry tire.
For
power, at some point you'll want to upgrade the engine, either by having it modded by a reputable drag-engine modder, or by swapping it out for something more powerful. The easiest swap is the OS .21tm, which isn't cheap, but it's worth every penny. You'll also want to ditch the EZ start for a pull start, or better yet, a bump start with a sealed rear plate. That thing is heavy and robs power. You'll also want to change your gears. Go with a 22t clutch bell, and a 70t spur. I'll double check that, I think that's what I have on my single speed car.
For
weight, this is where it gets fun. Ideally you want the car around 5-5.5lbs. You can go as low as 4.5 "legally", but traction will start to suffer. I think a stock Slash is somewhere close to 7lbs or just under. You can drop a bunch of that right away by swapping out the lower plate for a CF one. Xtreme Racing makes one that's really good. Dropping the EZ start will take away quite a bit. Get rid of the big gas tank and put in one from a Jato. You don't need all of that. You can also swap out the servos for low-profile ones to save some more weight. Get the super thin front tires and wheels, couple of companies make them, they are sold at aMain Hobbies.
You'll also need a wheelie bar. There are a few options out there, or you could just make one with a strip of CF and some ingenuity. Otherwise, the car will end up on it's lid after about five feet
Choose a good body that is known to fit well. Proline Corvette is popular. Remember you'll need either Bandit or Drag Slash rear arms to fit any of these bodies other than the super wide Parma ones.
Most importantly, don't listen to the electric guys who bash nitro. Most of them have daddy issues
Good luck!