You have invested a lot of money in that Memory Foam Mattress so it's important that you maintain it.  Of course, memory foam is nothing like a regular mattress.  How do you maintain it?  Should you flip it?  Does it need regular vacuuming?  All of your questions and more will be answered here!
Buy Your Memory Foam Mattress Some SupportCredit: http://www.flickr.com/photos/65407885@N00/321986856/

Support System

Since foam mattresses do not have any internal support structures, it's important that you have a study base for your new baby.  If it's not supported correctly, your mattress will stretch and develop a sag or dip in the middle. 

This issue can be solved by a good-quality box spring or bed platform.  Not only will this help protect your investment but will add some height to your bed, making getting in and out of bed easier. Most beds already come with bed springs or they can be easily added for an additional fee.

If you do decide on a platform bed, make sure the slats are at least half an inch apart to allow enough air to circulate around the mattress.  Foam is well known for absorbing body heat and can turn your comfortable bed into a sauna.  Having the correct air circulation can help solve this problem and keep you as comfortable as a bug in a rug.
Memory Foam MattressCredit: http://www.flickr.com/photos/foshie/2310561314/

Cover It

Though your Memory Foam Mattress usually won't absorb liquid as much as a regular mattress, it is still possible to stain it.  So, it's important that you buy a mattress cover for it and keep it on.  Stay away from the plastic covers – they can make your bed too hot and uncomfortable.

Turning

To even out wear and tear and extend its lifetime, customers are advised to flip their regular mattresses every six months.  Memory foam, on the other hand, is considered a "no-turn" mattress, and doesn't require to be flipped, though some say that a periodic turn wouldn't hurt. 
Memory Foam Mattresses Need Maintenance TooCredit: http://www.flickr.com/photos/kylepeyton/3813848880/

Vacuuming

Though Memory Foam Mattresses are known for being hypo-allergenic, it's still a good idea to clean it regularly.  To do this, break out your vacuum and run it around the top of your mattress.  You might even want to break out the wand attachment and run around the edges and sides to ensure you catch all of the dust mites and flakes of dead skin and hair that seem to be everywhere.

Smells

Memory foam mattresses can come out of the factory with a "smell" to them.  Don’t worry – this will go away with time.  When you first get it, leave it uncovered for a few hours to give it a chance to de-gas a little.  Every time you change the bedding, let it air out for an hour or so to help it along.

If your mattress develops an "interesting smell", sprinkle a little caking soda on the surface and let it sit for an hour or two before vacuuming it up.  Also, make sure to wash all of the bedding, including the cover.  This should help to alleviate the smell.