Your host probably has a lot on his or her mind, and if you can take care of a few simple tasks, you could provide much-needed relief. If your host is bustling around the kitchen when you arrive, ask if you can pitch in.
When a meal is over, clear the table and offer to do the dishes. If there are no limes for the drinks, offer to go to the corner store. Such gestures are helpful, but they also show your appreciation for all that the host is doing. And everyone likes to be appreciated!
If your host declines your help, it would be impolite to insist. Remember that some people would feel rude if they let their guests lift a finger. So ironically, it's rude for you to force them to accept your help (even if you have the best of intentions). If they do refuse your offer, you can try a second time, but if they ask you to sit down and relax, take them at their word. Renew your offer of help at another time.