I am astonished at how complicated and cryptic Ms. Raye's suggestions are. Maybe it's just me, but I don't think those posts answer the question asked at all, and frankly, if you changed the settings of the second router to use a different gateway, you'd get no internet access at all. So I don't think the info is correct.
As I read the question, the original poster simply asked how to set up a second router connected to the first that will also use DHCP. Now there's an easy way and a hard way. The easy way is to use the second router as an AP (access point) connected to the first router. The harder way is to put the two devices on different subnets (but still using the same gateway) and configure the second router so that it avoids double-natting.
The first way is so simple its ridiculous: Just connect to the second router and turn off that router's internal dhcp server and let the first router hand out a dhcp address to the second one. Make sure they are both set to use the same gateway address. You don't even need to worry about setting a static IP address on the second device (unless you really want that, or need port-forwarding, or are using SIP or VOIP phones on the network). Easy peasy. Now you can connect devices to the second router and gain internet access through the second device, which is essentially extending your network.
If you really want two separate, independent networks, so that devices on the 2nd router can't see devices on the first router, that's a bit trickier but not much harder. And I say that with a caveat, because we don't know the make, model or types of devices you are going to be using. But in general, there are two ways to go about this, and it's pretty simple. Linksys has a really simple page that describes the steps, along with some nice graphics, and anyone should be able to follow them without much difficulty, regardless of the brand of router you are using. See this link: http://www.linksys.com/us/support-article?articleNum=132275
A more in-depth, but just as simple and easily understood explanation is found at this article by Tim Higgins at Smallnetbuilder.com (which by the way, is a site that has tons of home networking info that can help anyone who is interested). See this article: http://www.smallnetbuilder.com/lanwan/lanwan-howto/24428-howtotwoprivlan
OP can't find the DHCP turnoff.. You can run multiple DHCP enabled NAT routers in series, I'm doing that here....
The first one has a 192.168.1.1 gateway and the second is a 192.168.6.6
Tracing route to google.com [184.108.40.206]
over a maximum of 30 hops:
1 2 ms <1 ms <1 ms DD-WRT [192.168.6.6]
2 1 ms <1 ms <1 ms 192.168.1.1
3 18 ms 9 ms 9 ms 220.127.116.11
Yeah, lots of things are possible, but that doesn't mean it's the right way to do it, or that someone who is evidently tech challenged should set up a double-natted scenario. Much simpler to just get into the D-Link, change a couple of settings and let it provide the wifi the OP seeks without screwing with the DG1670. At least IMHO.
An addendum to my last post to Ms.Raye about running two NAT router's in series, I also received a PM from the OP who asked how to set up two routers in series to run two separate networks, one exposed to the WAN side and the other a completely isolated internal NAT sub-network.
I responded that yes, it can be done, and Steven Gibson of "Security Now" from TWIT.tv at his GRC.com website has a page on the GRC site that describes exactly how to set it up. He promotes this (actually he also promotes a triple-NATted solution as well) as a secure method of isolating one's "internal" LAN from being accessible or vulnerable to WAN-side hacking, and suggests that in the "triple" set up, one of the internal networks be used for sensitive data, the other for other internal uses, and the network exposed to the WAN-side directly be used for IOT devices. Personally, it's not what I'd choose to do (I would probably just set up two separate networks, to keep the IOT separate from my internal stuff), but if anyone is interested, here's a link to a page at the GRC site that describes exactly how to set up two routers in series for two separately NATted networks.
His page describing NAT security, which also contains some schematics on how to set up three separate LANS is here: https://www.grc.com/nat/nat.htm
Would not recommend a NAT behind a NAT. Causes problems for some applications / games online and will definitely slow your speeds down a bit.
I would suggest using one device to do the routing & DHCP. The other one should not be routing at all, but could exist on a different subnet if you like.
Turn off DHCP on the second router. Let the 2in1 do it. You can assign it a static IP address inside a different subnet if that's what you want to do.
Hope this helps.