The Tempest is a very high-performance frigate with exceptional speed and maneuverability, as well as a considerable amount of energy firepower and it's iconic built-in drone.
Some notable defense issues exist; the small shield arc should definitely be taken note of, as the arc is so narrow that it can leave the ship vulnerable to the proximity detonation of and subsequent area of effect of flak, and given their fragmentation damage type this can be especially devastating to hull hitpoints if your armour was worn down by earlier fights. "Dancing" missiles and shots from an angle can also be dangerous. Adding the Extended Shields hullmod where possible alleviates this problem significantly.
The second issue with the Tempests' defense is that point-defense weaponry requires sacrificing one of the two medium mounts (potentially compromising offensive power), and then only provides protection in a limited arc. The Active Flare Launcher ship system helps with this issue, and a Heavy Blaster provides sufficient single-mount firepower that the second mount could be spared for PD.
When seen it is usually equipped with a Pulse Laser, a Graviton Beam and one of the standard missile weapons. This loadout alone is usually sufficient, but since it has medium energy weapons it can also use more powerful weapons such as the Heavy Blaster, but this requires care (and is thus not recommended for AI-piloted Tempests) due to its high flux cost.
This loadout's purpose is low-risk general assault. From my experience, it works nicely when used by AI.
When used by player, keep in mind that your system is Active Flare Launcher, it has relatively short cooldown, which allows you to use it often. I recommend using it for guided missile barrages that come at you. Tempest's speed allows it to dodge incoming unguided missiles and other projectiles.
Pulse Laser is your 'primary' weapon. Use it to raise flux of enemy ship to high level and force it to lower its shield. If you wish, you can use it to take down fighters, albeit it may be hard.
Phase Lance is your deadly 'secondary' weapon. Use it to finish off damaged enemies or to strike enemies right into hull, even better if you'll hit enemy in vulnerable spot and then use your Pulse Laser to strike at exactly same place, for maximum damage. Don't use it on shields, unless enemy is at almost 100% flux, because you'll waste a shot. Beams deal soft flux damage, which can be dissipated by enemy ship passively, it doesn't have to lower its shield to get rid of it.
Harpoon MRM is another of your deadly weapons. You have 3 missiles, so make good use of them. Use it to finish off enemies or strip them of their armor. Don't waste them on shields outside of very specific situations (enemy ship is almost overloaded, has its shield on and you want it to get overloaded, so that your other ships may exploit the opening).
Terminator Drone, while not exactly a weapon (it's a built-in drone on Tempest), can be considered as such. In current version (0.8.1a), it has a shield and is armed with Ion Pulser, which can disable parts of or even entire enemy ships, if drone is lucky. Send it to engage retreating ships, so that you or your other ships can deal with them or send an preemptive strike against an enemy ship to cripple it and make it an easier target.
It's also very useful against phase ships like Shade, because as long as you'll stay in drone's engagement range (1500 units), it will pursue said phase ship and will try to attack it, eventually crippling it by disabling its engines, which leaves that ship floating and vulnerable to any attack.
Only up to date for version 0.9. It is likely still broadly correct but not verified for the most up to date data yet. Please double check the Version History