OK, here goes. Remember that these instructions are for an HP Photosmart 7510 all-in-one wireless printer.
The first thing I did was disable the low-power sleep mode of the printer. I can't remember how to do this, but you should be able to find the information readily on the internet.
You will then need to make changes in 2 places, the printer and your router.
1) I'll proivide some screenshots below. You need to go into the printer setup and select networking. From there you get a choice for "Automatic" or "Manual". The default is Automatic. Change this to manual.
2) Provide an "IP Address" that is in the range of addresses you have selected for your home network.
3) Bring up your router manager window in Safari. Mine is a Netgear router, but yours will have similar functionality.
4) Reserve the address you picked for the printer and save the router settings.
5) You have now disabled DHCP for the printer and, in this case, assigned it an IP address of 192.168.1.110
6) Restart the printer and you should be good to go. This address is now reserved for the printer, and the DHCP server in the router will not try to assign it to anything else.