There are many types of pests that can create a problem for people. Some of these pests require specialized animal removal training, and others you can deal with yourself. However, it is important to be informed as to what you are dealing with, and what the options are.
If your problem is with domestic animals on your property, you are legally allowed to trap these animals and turn them in to the local animal shelter. To get rid of unwanted pets you can choose: Los Angeles animal trapping & removal All Star Animal Trapping.
Humane traps may be rented from the shelter in many cases, for catching feral animals. However, you must release any wild animals that you accidentally catch in the trap, back into the same area.
Feral cats can be a problem in some areas. You are allowed to trap these cats and take them to the animal shelter, however they are almost certain to be euthanized there, as they are not adoptable.
In some places, the shelter will spay or neuter and vaccinate feral cats for free, if you are willing to re-release them onto your property.
Spayed and neutered ferals are less likely to fight, will not have kittens every few months, and can be less of a problem all around.
Wild animals can be trickier. In many places, it is not legal to remove wild animals from your property unless they are meeting certain requirements for being a nuisance. These requirements may not have the same definition of a nuisance as you do, so look them up if you are considering this.