To expand a bit (and pulling from a PM I received):
An internet connection comes into your house (using DSL as the example) through your phone line. You plug that into a modem (that may also be a router) which connects you to your ISP. The modem/router will typically have a DHCP server built in. Access your router config (using something like http://192.168
.0.1 ; 10.0.0.1 or 192.168.1.1 depending on the brand and instructions) and turn off the built in DHCP server. If you have already done this because you put a separate router on your network (by connecting your modem/router to a new router) then you will simply disable the DHCP function in this new router (similarly to how you did previously). At that point your new router (ambiguously termed router refers to both wired and wireless routers) that was performing the job of a DHCP server will continue to perform all other functions including serving up the 'net wirelessly. Often times one of the configuration options are instead to change the device to a DHCP-Forwarder (which in simple terms means to disable the DHCP server in that device). That choice would be just fine, it just depends on the terminology your router uses; both turning off the DHCP server (Disable DHCP Server) and enabling DHCP-Forwarder are the same thing (similarly glass and cup represent the same thing).
Slightly more advanced network setups might include 2 wireless routers that "wirelessly bridge" a connection. The same would hold true in this network arrangement. One of the wireless routers will likely be offering a DHCP server currently. You would simply disable that server, the wireless bridge will remain intact.
The terms that seem to be most confusing are relating to routing. A router is a slightly more sophisticated device that 'routes' packets to their destination. Often times (and with newer equipment) switches will contain a bit of 'intelligence' that also routes packets to their destination which really helps to confuse and blur the lines of router/switch. So, a wireless *router* (when referring to home networking) is simply a router with built in wireless capabilities. A non-wireless router is simply a router with a built in switch (again just talking home networking equipment, industrial stuff may differ, but the idea is the same). A hybrid router (most often what you buy) is a wired router, a 4-8 port wired switch and wireless access point all in 1 device.
The same thing applies to every one of those devices. If you have multiple devices, you should have already disabled 1 or more DHCP servers anyway; and if you haven't, do it
In a really lame diagram, here is what it might look like:
--->DSL Modem/router (DHCP disabled)---->Wireless Router---->wireless devices
------->other wireless or wired routers (with DHCP disabled)
That second device that everything is connected to; that *should* be the only device in your network running a DHCP server (and if it's not, get your network setup so it is). Once you are ready to install LinuxMCE, disable that single DHCP server that was performing the DHCP functions for the entire house. Then, when you install LinuxMCE on your core machine (that is probably wired to one of your routers, preferably your main router via a gigabit connection) it will begin performing the DHCP server functions.