Apple's "extend" feature uses proprietary settings that are designed to only work with other Apple routers.
So, it would be extremely unlikely that a D-Link router.....or any other router, for that matter.....would be compatible with an Apple product if you are trying to "extend" using wireless only.
All you can do is configure the D-Link device according to the D-Link manual to see what happens. But, unfortunately your chances of making this work are quite close to zero.
The odds improve greatly if you can establish a permanent wired Ethernet connection between the Time Capsule and D-Link router.
Bob's advice is spot on, but it may not be apparent that the bandwidth (speed) you'll achieve with the extended range configuration will be significantly reduced using a wireless-only architecture. If you were to add an Airport Express (no wires) and put it in between the Time Capsule and the area in which you need more coverage, the Express will be working as a repeater. First, it receives a wireless packet from the TC. Then it retransmits it to your Macs or other wireless clients that are more distant from the TC. And vice versa for packets coming from your distant Mac. The TC will receive each packet, and retransmit it to the TC. The repeating function cuts the throughput in half, more or less.
A much better way to extend the range of the Time Capsule is to run an ethernet cable from the TC to the area where you need better coverage, and connect it to another Access Point (D-Link, Linksys, Netgear, etc). Since no repeating function is performed, you'll get full WiFi throughput in the extended region (whatever is the speed of the added AP). Of course, running a cable may not be possible given your physical environment.