remind

Remind and remember are not the same. If you remind somebody about something, you make them remember it. Thus, remind is a transitive verb, i.e. it always has an object which may be followed by to + infinitive or a that-clause. Compare the following:

Remind me to send Denny an email about the change of dates.
I reminded them that the dress rehearsal had been brought forward to Wednesday.
I shouldn't need to remind you to wash your hands before you sit down to eat.

When you say that somebody or something reminds you of something, you associate it with a memory from your past:

She reminds me of The Princess Royal. They are so alike in looks and appearance.
Doesn't this countryside remind you of Cornwall? It does me.
I think I know which one it is, but remind me of your house number.

Remember

If you remember something, you recall people or events to your mind. Remember can be used transitively with an object or intransitively without an object. It is often used with to + infinitive and with when- where- or that-clauses. Compare the following:

Do you remember the first time we sat under the stars, listening to Beethoven's Ninth?
Do you remember when we first ate wild mushrooms? ~ Yes, I remember.
I can't remember where I've put the spare set of car keys. Have you seen them?
Will you remember to collect your suit from the dry-cleaners or shall I do it?
She remembered that she was going clubbing that evening and cheered up.

remember + infinitive or remember + verb-ing?

A lot of readers ask about verbs that are followed by verb-ing forms or to + infinitive. Some, like want, decide, agree, are always followed by to + infinitive. Some, like look forward to, enjoy, finish, are always followed by verb-ing forms.

I decided to turn off the computer and go home. I would finish writing the report tomorrow.

Some verbs can be followed by either verb-ing forms or to + infinitive, sometimes with some difference in meaning. Remember and forget are two such verbs. Remember and forget with an infinitive always refer forward in time. Remember and forget + verb-ing forms always refer back in time. Compare the following:

I don't remember talking to you about Terry's divorce. I don't even remember you asking me about that.
I shall always remember flying to America on Concorde.
Remember to close all the windows and lock all the doors before you leave the house.
I forgot to warn him about the dangerous dog and he was bitten.
I shall never forget sharing a bottle of iced water with you beside the Pyramids in Egypt.