“It only takes me about 15 minutes.”

You're out to lunch with a group of coworkers and talking about your daily routines. One coworker says that her commute to work is 45 minutes long. You want to continue the conversation, so you tell how long your commute time is. You say:

It only takes me about 15 minutes.

it takes (somebody) (a length of time)

This is a phrase for saying how long a common process or action is. It often expresses how long a person's daily commute to work is. But it can also be used to talk about other actions, like taking a shower, getting dressed, and puting on makeup to get ready to go out:

It takes Erin an hour and a half to get ready.

only

In this case, "only" is used because 15 minutes is not a long time compared to most people's commuting time.