“How do you know if your teeth have shifted?”

If they changed their position from how they were before many months or years ago, they shifted.

As we get older, teeth will definitely shift if you aren't wearing a retainer. 

Something must have prompted this question, so either you're visibly noticing movement occurring in your teeth, or they feel different than they used to. You should ask your dentist if you're not aware of any esthetic changes in the appearance of your teeth.

I am glad you are interested in the health of your teeth. You may be asking this question due to a change in your bite. People with an over closed bite sometimes mention a change in their bite. In this type bite, when biting together, the biting edge of the lower front teeth fit up under the upper front teeth. This forces the lower jaw back and pinches tissues in the back of the joint. This jaw wants to be more forward. This gives the sensation that the bite is off and teeth have shifted. Supporting the lower jaw more forward with an oral appliance can help the jaw be more comfortable. This would help the bite feel more comfortable. A more forward jaw also brings the tongue more forward, opening the air way for improved breathing and sleep.
Excellent information about this subject is available in the book: GROWING A HEALTHY CHILD, SECRETS FROM A WISE OLD DOC
Thank you for asking this interesting question.