From TornCityWiki

Attacking is a good way to gain (Merits) and experience. Weapons (Weapon list) make attacking a lot easier, but the most expensive are not always the best in combat. Attacking uses up 50 energy (25 just after taking Vicodin), and is an essential part of the game. (especially faction life.)

UPDATE

A completely different and new way to attack was implemented by Ched (the mayor/dictator of TC) in late '08 to early '09. I, m00nshaed, am diligently attempting to overhaul all the outdated info on the wiki, but have not quite gotten to the attacking page. Please have patience, or better yet, update the info on your own. However, you should be advised, that while many tid-bits of advice on this page are sound, the mechanics of 'attacking' (so much fun btw) are quite different than outlined below. Thanks!! :D 10/7/2009

The user list will sort all the players in Torn City by level and sub sort them by player ID. To find the best targets you should look for people with high player ID's that are at or above your level (as it gives you the most experience).
High IDs mean that they have not played the game as long as the lower IDs meaning they most likely don't have great stats (speed, strength, defence, dexterity) so you are more likely to win.

Once you have found someone, click on their name and view their profile. Underneath their picture on their profile there are a list of buttons. You are looking for one that says Attack.

When you begin your attack you will get to choose which weapon you want to attack with. After each round you get to select your weapon again.

Ammo
Ammo is quite expensive, but guns cause much more damage than melee weapons (for the price). You must be very careful when going to attack that you have enough ammo if you want to use your weapons - as reloading will take a turn and give them a free shot at you.

You will see a battle report after each hit

1. Using your weapon you fired X bullets at player name for 1274 (1684)
2. Using his melee weapon he hit you for 456 (2346)

The numbers in the brackets are how much life you and your target has left. Melee weapons don't use ammo; if you don't have one you will only have your fists to use. Fists do 1 percent of your strength as damage. If your opponent takes you to 0 life, you will end up in the hospital. If you win the battle (taking your opponent to 0 life) you will have 3 options:

Leave them:
If you leave them you will gain experience and they will go to hospital for a small amount of time. You gain the most experience if you just leave them.

Mug them:
If you mug them you will steal some of there cash (1-10%) and gain only half the experience as if you left them. They also go to the hospital for a small amount of time You can improve the amount of money you steal by using merits.

Hospitalize them(aka Hosp u):
If you hospitalize them you will send them to the hospital for a long period of time. You will gain no experience from this. This is mainly used for gaining respect during war or revenge. If you hospitalize someone then they might get pissed and do it back. You can increase the time you put someone in hospital by using merits

Other Outcomes:

Stalemated: You will notice that beside each hit you make and each hit your target makes on you there is a number besides it. If this number reaches 50 then you will walk around in circles and neither of you will win the battle or gain any experience. 50 energy is not used if a stalemate occurs. DO NOT CLICK RUN AWAY IN EVENT OF A STALEMATE

Losing Attacks: If you lose an attack then you will go to hospital for a small amount of time and the person you attacked will gain experience. (You do not lose any experience)

Being Attacked by Someone: If you see you have been attacked by someone. This means that they have made a stealth kill. They managed to kill you without you being alerted before the attack. A player has named themself "Someone" exactly because of this.

Attacked with no event: This is because the person that did the attacking mugged, opened the wallet and nothing was inside, muggings that come up empty do not leave events, although you can find the attack on the attack page in your faction.

Another thing about attacking is: I have noticed that there are sometimes when you get an event saying that xxx attacked and killed you, you can sometimes turn right around and kill them. This is because the person who is on Defence of the attack, his/her stats are lowered. I do not know how much they are lowered by, but I do know that it is quite a bit, or else if you attacked them back, you'd stalemate. The other reason behind this (not normally) could be because the other person used a Drug, which the effect of them result in different stats being increased while another stat being decreased for a certain amount of time.

Defending: When a person is attacked, each round of combat will randomly pick whether to use a Primary, Secondary or Melee weapon. If you are lacking one of these, you will use your fists (which does very poor damage) when that weapon slot is randomly picked. This means that for defending it is generally better to have three reasonable weapons equipped than 2 weak weapons and one stronger one.

The high level players of Torn City say: "Don't attack until you're level 20. Otherwise you're a n00b and should be hosp'd."