If I train my pet using food or other rewards, won’t they only do what I ask when I have a reward for them?

This is a common misconception about reward-based training. When we are initially working on a new behavior, we reward every successful repetition, but very quickly we wean away from having the reward visible, and away from continuous reward. I will teach you the methods to facilitate this transition, and over time you will achieve what is called a "random reinforcement schedule".

Essentially, this means that the animal will never know which repetition of the behavior gets rewarded, so they continue to do what you ask in the hopes that this will be the time. To give a human example, it's like playing the slot machines. No one expects to win every time they pull the lever, but they keep doing it in the hopes that this will be the time they win it big!

In studying the learning process, behaviorists have found that behaviors which are randomly rewarded actually become stronger than those which are continuously rewarded. Imagine you are used to getting paid exactly every 2 weeks at your job. If you suddenly don't get paid on the day you expect, how likely are you to continue working? If you were used to being paid every two weeks give or take a few days, then you wouldn't necessarily be upset if the check didn't appear at exactly the two week mark. This is the same principle we take advantage of with weaning away from rewards for behaviors our dogs know well.

I do recommend occasionally rewarding your dog for known behaviors to help keep them on their toes, but the interval between rewards increases over time. I don't work for free, and don't expect my pets to either. However, I will take advantage of things such as play, attention, their regular meal ration and use those as rewards. (These are what's known as "life rewards".)