How can I induce dreams at night that I will remember when I wake up?

Keep a pen and paper by your bed. As soon as you get up, start writing what ever is in your head.

like she said. it may take a while, but you will eventually remember all (or almost all) of your dreams.

@Judi is right on the money here.

Yup, just keep a dream journal. Write everything you can remember as soon as possible because the amnesia after waking can wipe it away pretty quickly.

This assumes that we always dream every night. Do you believe this to be true? Does dreaming more often just mean, remembering the dreams the you have? Or, if you’re of the belief that we don’t always dream—how does one dream more often?

I do believe we dream every night. It’s the amnesia that keeps us from remembering them all of the time. I know I have several dreams a night, but can only remember partial bits of each one.

The Six Basic Steps
1) Doing the Mental Prep-Work
2) Increasing dream recall
3) Keeping a dream journal
4) Becoming familiar with your Dreams
5) Adding Awareness to your Waking Consciousness
6) Linking your Awareness to your Dreams

http://www.consciousdreaming.com/lucid-dreaming/how-to-lucid-dream.htm

Before you go to sleep, tell yourself “I will remember my dreams when I wake up.” If you’re consistent with it, and really want it to work, it usually does.