Team fights are where DK shines. He is a team-oriented hero that usually moves together with his allies to achieve objectives (push towers, team fight, get Roshan etc.). Before engaging you should always try to have your ultimate up. Without the spell, DK is much weaker and it isn’t advisable to fight with your Dragon Form on CD.
Starting a team fight:
DK can be a good team-fight initiator thanks to his Dragon Tail stun in combination with Dragon Form. You usually want to use your ultimate just as the fight starts. Don’t use it for instance right when your team uses Smoke of Deceit or to simply increase your movement speed around the map - having your ultimate up during the whole fight is essential and if you still have it up after the fight you will be able to use it to destroy buildings.
Your main initiation tool would be the Dragon Form + Dragon Tail combo. Activate your ult and try to stun and nuke down the disabled target with the help of your team. Alternatively, if you don’t have initiation items like Shadow Blade or Blink Dagger, it might be better to let another teammate with better initiation start the fight. You can, for example, follow up a Hex initiation by an ally with your stun and so not let the enemy use a defensive item/ability to survive.
Movement and positioning in a team fight:
Generally, the position of DK is in the middle of the fight. You are usually not trying to chase a single target to bring it down because you don’t have the mobility and damage in most cases to do so. Rather, it is better to stay close to your allies and provide control to allow them to deal a good amount of damage in fights while hitting and trying to nuke down targets that are close to you. Use your stun on high priority targets – enemy squishy carries or targets that can be brought down quickly with the help of allies. For example, heroes like Gyro or Storm Spirit are quite vulnerable to your stun initiation, since they are squishy and can be brought down quickly if they don’t use their BKB in time. Initiating on tanky heroes like Centaur or Wraith King might not be a good choice since they can survive your stun and counter initiate.
It usually is a good idea to use your Breath Fire spell on the enemy carry right when the fight starts. The 8 second damage debuff will reduce the damage output of the enemy hero during the fight. This is especially important versus stat-heavy heroes (Morph, Lancer) or heroes with high base damage (Tiny).
Since you are quite tanky, you should stay and fight – even if you get focused, bringing you down takes a lot of time for your opponents, which in turn give your allies freedom to deal damage and bring down the enemy heroes. This means that you rarely want to run away and usually want to stand your ground and fight. Nevertheless, if you have to run you can use your decent Dragon Form MS and stun to try to get away.