All military actions are usually done in groups of threes, or divisible by three, in both hand to hand combat and in ship combat. Space patrols, however, are done in groups of twos. On some special missions, like the Jem'Hadar ship flying through the wormhole in "The Jem'Hadar", can be done by a single ship.
Jem'Hadar warships are equipped with forward firing phased polaron beams and missile systems, able to fire both forward and aft. They have very strong shields, able to withstand phaser fire by a Galaxy class starship. Additionally, the locking of tract or beams is not possible on these ships. Dominion ships do not use cloaking devices, although the Dominion certainly had access to some. There are 42 Jem'Hadar and one Vorta aboard a ship. Standard space combat tactic is to concentrate fire on the other ship's warp nacelles (or other propulsion systems if they don't have warp nacelles), causing serious power losses. Many small ships are built rather than few big ones. Operating in teams, they can establish a continuous fire on the enemy's shields.
In ground combat, Jem'Hadar make extensive use of their cloaking abilities to get closer to the enemy. However, they don't cloak while in a battle. Standard ground combat equipment are polaron rifles and pistols. Alternatively, they can make use of blade weapons and are quite skilled in it.
The Dominion is very advanced in genetic engineering. They designed their soldiers, the Jem'Hadar, and even the Federation can't find a way to break their dependence on the enzyme. The Federation doesn't even know how to create the enzyme. Cloning is used, but it is not known how extensively it is used. They are apparently very advanced at it, being able to create a full-grown adult in at most a few years.
Originally, Dominion weapons were able to penetrate the Federation's shields; however, the Federation has found a way around that. Dominion transporter technology is vastly superior to the Federation's. We still don't even know where Eris beamed to; probably through the wormhole. Additionally, in "Heart of Stone", the Dominion's transporters worked when the Federation ones couldn't.
Their shield technology is superior as well. Standard phasers can't penetrate the shields of a Jem'Hadar warship. Also, these shields prevent Federation ships from locking a tractor beam. Jem'Hadar are able to ignore containment fields, probably a result of the shield technology as well. Dominion technology is able to detect cloaking ships if they move above a certain speed, using anti-proton scans. The Dominion doesn't call the wormhole "wormhole", but rather "anomaly" or "passageway".
Dominion Planets
Callinon VII The Dominion maintains an unmanned subspace relay station there. O'Brien and Dax were captured on that planet after sending data up to the Defiant. [Search I]
Karemma Homeworld of the Karemma. According to the novel "The Search", it is a world of mercantilists. Tulaberries are most likely produced on Karemma; additionally, there are weapon factories there. Karemma is about 0.524 lightyears away from the wormhole.
Kareel Prime We actually don't know if this planet really exists or not. If we assume that Eris told the truth about that one, then Kareel Prime is the Vorta's homeworld.
Kendi System and Obata Cluster There is not much known about these star systems, except that a Jem'Hadar patrol left the Kendi systems heading to the Obata Cluster in [The Quickening].
Name Unknown A planet 1.29 lightyears away from the wormhole at maximum. Cmdr. Sisko, Jake Sisko, Quark and Nog visited this planet for a science project for Jake's and Nog's school in [The Jem'Hadar]. There, they were captured by Jem'Hadar forces and were allowed to escape later. The planet is rich on resources. The course to the wormhole from this planet is 171 mark 259.
Name Unknown Another homeworld of the Founders, with significantly more Changelings living there compared to Omaria. It's exact location and name is unknown. First seen in [Broken Link].
Name Unknown The homeworld of the Tarogarans, the people who enslaved the Skreeans, which was invaded by the Dominion prior to the events in [Sanctuary]. It's most likely part of the Dominion now.
Omaria One of the Founder's homeworlds. Omaria is a rogue class M planet without a sun, located in the Omarion nebula. A part of the Great Link was present there when Odo found this planet in [Search I]. Large parts of the planet's crust were destroyed by a combined fleet of Romulan and Cardassian ships in a failed attempt to wipe out the Founders in [The Die Is Cast].
Vendros IV A planet where Dominion scientist discovered a Gateway built by the old T'kon empire. Jem'Hadar rebels captured it. To avoid letting these Jem'Hadar use the gate, it was destroyed by a combined team of Dominion and Federation forces. [To the Death]
Dominion Ship
A Jem'Hadar
Dominion Symbol