Holding the trigger down and spraying bullets is not recommended, as the strong recoil of the weapon can easily waste of a lot of ammo. Firing short bursts helps to increase your accuracy. Aim low when firing longer bursts to compensate for recoil.
If you're leveling the weapon and running low on ammo, remember that weapons gain experience for assists as well, so one can damage an enemy with just one shot and then finish him with other weapon (Melee is recommended to avoid the switch time).
Using Rifle Ammo Mutation can also help to recover ammo lost due to the weapon's habit of burning through ammo quickly. Alternatively, use Rifle Scavenger or Team Ammo Restores.
There are various mods you can use to counteract the Grakata's high recoil.
Stabilizer is recommended as it reduces the recoil without compromising its fire rate.
Critical Delay can be used as an alternative as the increased critical chance brings higher damage output and the lower fire rate decreases the recoil. However, this will lower overall DPS.
Vile Precision can be used as another alternative, reducing both recoil and fire rate. It will increase accuracy on medium and long distances, albeit at the cost of lowering overall DPS.
Heavy Caliber is a good choice for the Grakata, as the weapon's deceptively high accuracy mitigates the accuracy penalty generated by the mod, reducing the overall bullet spread.
The Grakata will benefit the most from Hammer Shot, as the weapon has a very high status chance compared to most fast-firing primaries. It will also receive a decent critical damage boost.
Due to its high status chance and incredibly high firing speed, Grakata is able to proc many status debuffs rapidly.
Although a large portion of procs will be physical-damage based, Grakata is still easily capable of causing all possible debuffs in a single burst.
Area-of-effect procs such as Gas and Electric damage are effective at all levels. Electric can also be used to stun targets.
The Gas & Electric combination can be remarkably effective against thick swarms of lower level light Infested.
Grakata is ideal for rapidly stacking Corrosive effects to quickly strip higher level enemies of their thick armor, or for using Radiation for crowd control.
To significantly decrease time-to-kill for higher level content, the Viral or Magnetic elemental procs are recommended, to instantly reduce an enemy's health significantly.
Note that besides Corrosive, most procs do not stack, which can still severely limit Grakata's effectiveness.