The rules of Team Deathmatch are nearly identical to Deathmatch, with one exception: players fight against each other on teams. The two teams will then fight to reach the score limit. In TDM, the primary objective is to amass more frags than the opposing team.
This concept of a team, combined with the rules of deathmatch, are the core of all other gametypes; the difference being added objectives like "Capture the Flag" or "Destroy the Power Core."
Maps are rarely made specifically for Team Deathmatch because TDM can be played on DM maps, and so a DM map will reach a larger audience. However, those that are targeted towards TDM are often larger than DM maps (but still smaller than maps for most other gametypes). An average playercount of about 8-16 is normal, but occasionally maps are made for 4-24 players. Maps which support more than 24 players are rare because of the immense size and the resulting time they take to create and the time they take to download.
Like in Deathmatch, most TDM maps are set inside or in a closed area, with a wide variety of themes. No vehicles or turrets are supported. Adrenaline is on and the translocator is off. Instagib is fairly popular for TDM.
TDM maps usually don't have superweapons, but when they do it's usually in a difficult-to-reach spot. Depending on the size of the map, there will usually be about 6-9 weapon types. Players usually spawn near weapons, but spawnpoints are also usually fairly far from each other and in somewhat protected areas (which mainly means that you probably won't spawn in the middle of an open floor). Spawnpoints are not team-specific.
Usually the number of hitscan weapons is approximately the same as the number of spam weapons. Common weapons include all standard "deathmatch" weapons. Low-level powerups are common and usually easy to find, but more powerful ones like the UDamage, Big Keg-O'-Health, and Supershield are either difficult to find or not implemented at all (usually smaller maps will not include them, but larger maps will).
To determine the winning team, the total frags (kills minus suicides) of each player on a team are added together and compared to the other team's frags; the team with the higher fragcount wins. This method means that a single awesome player can often carry a team, or conversely if teams are fairly even, a single weak player can drag the rest down.
Because of the size difference, TDM maps tend to be more open than cramped. This means that hitscan weapons are often dominant. Also, "team tactics" are supported which means that players often travel in groups for security and firepower. Often one player will use a sniper, shock rifle, or minigun while the other will typically use one of the other weapons to provide a balance between hitscan and semi-spam. The down side of this supportive method is that traveling too closely can result in splash damage effecting multiple teammates.
"Team Deathmatch is just like regular Deathmatch, except that the players in the map are split up into two teams. A team's score goes up one point every time a player from the other team is killed. The team that reaches the predetermined score wins the match."