You are unlikely to get in a dream within 10-20 min, but you may see hypnogogic imagery, it is pretty cool, sometimes you can even change it.
It's pretty easy to get early in the morning, especially if you didnt have enough sleep the night before and there's something preventing you from completely falling asleep. So what you do is close your eyes and relax. You are falling asleep, but something is keeping you awake, as a result you are right in between dreaming and being awake. After a while you become aware of the visuals before your eyes, changes in your mind and other weird things.

If this wasnt clear, here's an example:
You sit in class and the lecture is boring, the professor sux, but the material is kinda important. You can probably learn it from the book anyways. So you close your eyes and sit there. WIthin 3 minutes the professor's voice seems different... It is distant and slightly distorted. You may even continue to listen to it. Within 10 minutes you realize that you are somewhere else entirely, no longer in the classroom, even tho you can still hear the professor. As this thought hits you, you may realize that you are back in the classroom, except this time you can see it with your eyes closed... There's an exact replica of the classroom hovering before your eyes, you can shift your *dream* eyes around and focus on different parts of the picture... You can change the picture as well, just do it slowly, dont rush the change.

This technique requres a bit of practice, but it is pretty entertaining, particularly cause you are almost fully aware that you are starting at the hypnogogic imagery and there's no grogginess of sleep...