Nomenclature:
A round is the time that it takes one side to finish each person's turn.
A turn is 2 minutes. You can move and take one or two other actions within a turn.
All "To hit" rolls are resolved by rolling a D20, with various modifiers from stats, skills and items added. The goal is to get a number equal to or greater than the target, which is usually the target's armor class, or AC. For example, if you're shooting at a Mage with an AC of 7 and you get a 9, you hit them.
Damage is rolled according to the weapon, unless there are special rules in effect. For example, certain types of armor reduce damage from a type of attack, so a 5 might become a 3.
A critical hit occurs when you roll a natural 20. It always hits, and it adds an extra die to your damage roll.
Lethal and Non-lethal damage:
Non lethal damage is done either with fists (Assuming that you aren't wearing brass knuckles or something like them), or by choosing to use certain weapons to do so. Guns and bows cannot be used to deal non-lethal damage unless you choose to use them as melee weapons. Swords and knives can only be used as non-lethal weapons if you take a -5 to hit on attack rolls, as they are edged weapons and you would have to hit with the flat or hilt, neither of which the weapon is designed for. (Reasonable measures to alter this should be effective). 1 point of lethal damage is done for every 5 points of non-lethal damage. It is usually used to knock out someone, or give them a minor injury.
Lethal damage is done by most weapons. It is used to kill or seriously injure someone.
Melee Combat:
Grappling is resolved by making an opposed Strength test against your opponent. Opposed tests are handled somewhat differently from normal combat - you and your opponent both roll a die, and the person with the higher number wins.
Edged melee weapons can be deflected by making an opposed Agility roll, if using a melee weapon or rifle, though the latter entails a penalty of -2. You can also disarm an opponent, but cannot use a rifle to do so. All of this applies to blunt melee weapons as well, but they can be deflected or disarmed barehanded. Unarmed opponents cannot be disarmed in the literal sense, but they can be deflected as though a blunt weapon.
Thick clothing will halve the damage done by unarmed blows, and blunt melee weapons will do 3/4 normal damage against it.
