Applying a light texture, such a a sand texture, will help cover many of the uneven patched areas. Expect some to still show through. You could also apply a heavier texture paint that will have a better time covering this up. Many manufactures make a texture paint already mixed and ready to go. Another option is using drywall mud, thinned, and either a texture roller or stomping texture brush for a thicker more pronounced look.
Most boxes of this texture are designed for 2 gallons. It should say on the container. If not, mix half with a gallon of paint and see what it looks like. You can add more for a more dramatic look. You can remove the texture before it dries with a wet rag and water.
Apply with a paint roller in one direction only. This is important, rolling back and forth with produce an uneven look. Also mix the paint often. The sand settles out of the paint quickly, ending up on the bottom of the bucket.
Many manufactures make a pre-mixed paint that has the texture already in it. This is a little easier to use and there is no guessing about mixing ratios.
Texture paint is available in different consistencies for different effects. It's applied with a roller, often the manufacture has their own special roller for this purpose.
Drywall Mud Texture
There is a lot of possibilities with drywall mud. The easiest textures are using a special texture roller, different patterns are available, or a texture brush. This will require a little experimentation, but drywall mud is cheap and the roller or brush can be used over and over.