Need to connect mac-mini and thunderbolt display to a Dell U2713HM for dual monitor 2560x1440
HDMI is out because the Mac Mini's HDMI port maxes out at 1920x1200. You're going to need to grab an adapter to go from Mini-Displayport to either dual-link DVI or Displayport, which are both supported by the Dell.

Now, the Thunderbolt display can't directly output Mini-Displayport for boring technical reasons (see question 20). There must be a non-display Thunderbolt device between the display and the adapter I mentioned above. The cheapest example I've found is the Seagate GoFlex Desk Thunderbolt Adapter (STAE122), which has two Thunderbolt ports for daisychaining and retails for about $180.

The full chain:
Mac Mini -> Thunderbolt Display -> STAE122 -> MiniDP to DP or DL-DVI adapter -> Dell monitor