Nobody likes paying attorney's fees. Not even your own client when you win (they'll tolerate it much more, but they won't like the bill). In litigation, you need to plan on paying your own bill. The predominant exception is a contract clause.
Parties are free to contract. Included in that right is the right to agree to a contract clause that requires the other party to pay your attorney fees if you prevail. Absent this sort of clause, you generally do not have the option of forcing the other side to pay your bill.
Certain other costs of litigation are collectible if you prevail at trial. Those costs include deposition fees, filing fees, and witness appearance fees.
You can control your contract terms. Use that control and get a very beneficial attorney fee provision in your contract with my drafting help. It will substantially increase your leverage in a dispute and can reap big rewards for you.