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First you start out with a horse with high enough GP, you can either work up to it by breeding or buying in sales.
If you have a female, you can check the public coverings and make sure you cover your mare with a stallion with very similar or higher GP. Please note that GP only increases if the BLUP is 60 or more. If it is below 60, your foal will have a lower GP and poor skills.
You can then use your foal if it's a male to breed back to your female. This will continue the GP increase. If you get a filly as your foal, you can continue finding higher GP stud coverings.