Buy the matching box-spring foundation for your new mattress. Specific box springs are designed for specific mattresses, so replace your old box spring when replacing a mattress. Make sure the mattress and box spring are level and securely placed on top of a proper frame. Uneven mattresses and frames can cause premature wear to the mattress and discomfort for you.
Give yourself a little extra time the first few nights. Go to bed earlier than usual to compensate for any trouble you might have falling asleep. Make sure the temperature in the room is cool enough to sleep comfortably.
Move to other areas of the mattress if you feel like you are sinking in the center or not getting enough support near the edges. After two weeks, if you still don't feel properly supported, consider trading in for a firmer mattress.