This document is by no means complete, and should by no means be refered to as an absolute authority on the gameplay of Doom.
Contents
Controls
Before you start to play, visit the controls section of the options menu to change your controls to resemble a more modern control scheme. With a few changes, you can be playing Doom just like all your other games, with a keyboard and mouse.
Movement
In Doom, there are several 'bugs' in regular movement that have over time been come to be known as features of the Doom engine. See The Doom Wiki for completeness.
Straferunning
By pressing Forward and Strafe Left or Strafe Right at the same time, you move faster than you would normally by just running forward. This is basic movement, and once practiced almost becomes second nature.
SR50
By straferunning, and at the same time pressing a button on your mouse to enable mouse strafing and moving your mouse in the same direction as your straferun, you can move even faster. While in SR50, however, you can not turn around, so you sacrifice aim for mobility. This is a more advanced maneuver, and is harder to control, but it is useful at times.
Backwards Movement
It's use is limited, but in Doom moving backwards is actually faster than moving forwards. Straferunning backwards, as you can imagine, is proportionally faster.
Wallrun
If you straferun at a certain angle close to a completely flat wall going from north to south, or from east to west, you actually gain even more speed. There is a server setting that allows wallrunning against walls in all cardinal directions, but by default, wallruns are only one way.
Weapons
Weapons in Doom are differently balanced than in most other games.
Super Shotgun
This is the weapon that you will most likely use often. They are usually plentiful on any given map, and an accurate shot can kill an opponent in one hit, but it takes a second or two to reload, and is inaccurate past a few player lengths.
Chaingun
This weapon is most useful at long range, or to chase down a fast moving player. It has the distinctive ability to constantly disorient an opponent from the near constant amount of redscreen buildup it gives the other player, which can affect his or her aim. The first couple shots out of the chaingun are the most accurate, while subsquent shots are less so, therefore to maintain accuracy with the chaingun one must tap the fire button instead of hold it.
Rocket Launcher
This weapon is useful as it is highly damaging to other players, and has a respectable amount of splash damage. However, unlike rocket launchers in modern games, the rockets this weapon fires are slow, so slow that a straferunning player can actually outrun their own rocket given enough space. Useful in the same way a grenade is in a modern game, to flush opponents out.
Plasma Rifle
A very powerful continuous stream of damage, being hit with more than a few of these balls of pain can be a painful experience. However, although faster than rockets, it is still possible to dodge plasma, especially in areas where there are a lot of obstacles. Therefore, use this weapon as if you were watering a garden, for lack of a better expression.
BFG 9000
This weapon is often criticized for being overpowered, but in a 1on1 game this weapon is considered balanced. For a full explination on how the BFG works, please read The BFG FAQ. Once you learn how this weapon works, it is remarkably easy to dodge in a 1on1 fight, or if you know it's coming.
Shotgun
Relatively weak weapon compared to the Super Shotgun, but its tight pellet spread does not decay at long range, making it a decent weapon to 'ping' people at long range with.
Other
There are four other weapons, all of which are of dubious value. The pistol is far too weak to even consider trying to kill someone with. The fist, beserk fist and chainsaw are too hard to land hits with, and if you're close enough to punch them, you're more than close enough to deliver a killing shot with a Super Shotgun. There are two situations these weapons will likely be used in, desperation and comedy.
Items
Doom has two main ways in which items are handled by the engine.
Deathmatch
In normal deathmatch, weapons stay where they are, but all other items, such as ammo and health, do not respawn after being taken. In a 1on1 situation, this forces players to carefully consider and save items for times when they need it. In FFA, it doesn't really matter anyway, since you have lots of ammo when starting out, and you'll probably be dead before needing ammo again.
Altdeath
In Altdeath, all items, including weapons, respawn after 30 seconds except for invulnerability and invisibility spheres. This leads to the item control gameplay seen in other populat deathmatch games, but has fallen out of favor in the Doom community.
Capture the Flag
Capture the Flag handles item placement in a way reminiscent of more recent games, with weapon stay and item respawn. Since CTF is a relatively new mode of play in Doom, this modern standard of item spawn has been adopted.