What d-link modem is it, I mean what model?
The modem hands off to the router unless you have some weird off the wall ISP that uses nonstandard equipment.
After the router gets the signal then it uses DHCP to send to the devices.
The modem should also use DHCP, it not then I suggest telling your ISP to fix the junk they gave you.
Standard is: the line comes into the house, it can be dialup, DSL, cable or dish, makes no difference, the signal is standard, it goes into the modem where it is turned into a signal that computers and router use, the router sends it out to all the devices on the net work.
That is how it works.
If your modem will not work with a router then trade that useless modem for one that will.
The way I describe above is how it works.
I have Time Warner Cable into the modem, it is connected to an Apple Airport Extreme, from there it goes to 1 Power MAc, 4 Macbook Pros, 1 iMac, two PlayStations, 1 XBox and 1 PowerBook.
So I know how this stuff works.
If your modem refuses to act correctly then trade it for one that does, all routers are the same as for function, features vary.