It's basically a time sink. You have experience gained from doing crimes and fighting people, to go up in level.
The more crimes you do, the more crime experience you get and the bigger your nerve bar(ability to do crimes) goes up.
Your fighting stats are improved by training in a gym. There are four than you can train, strength/defense/dexterity and speed. They all affect a fight in different ways but it is always better to have them balanced in number.
You can join a faction which is like a clan. In there you can make friends and war together. War is when you fight other factions to gain respect. Respect is a currency in which you can buy upgrades for the faction that give boosts to all its members.
Overall, it's just a numbers game. Everything runs on a timer. Cooldowns if you will. Money is another number used to buy weapons, armour, drugs(helpful in the gym).
If you ever want to take a look, sign up. Use my referral code of course, http://www.torn.com/1208641
Go immediately into those forums into the guides and tutorials section. Getting an early start is a big plus. A good start is all knowledge. Learn the game quick and you can succeed.