I would start by learning the basics of HF propagation. CQ Magazine's "The NEW Shortwave Propagation Handbook" is excellent, but there are plenty of online sources that Google will locate for you; check out Bob NM7M's comprehensive (though somewhat dense) tutorial on the topic.
There are two kinds of software tools available to help DXers with propagation:
1. tools that forecast propagation based on ionospheric models and current solar conditions
2. tools that monitor HF beacons (like the IARU/NCDXF beacon network) to assess actual propagation
Since ionospheric models are imperfect, its best to calibrate forecasts with actual propagation.
Classic forecasting tools like IONCAP and the more modern VOACAP require lots of numeric input; IONCAP produces numeric output, while VOACAP produces both graphical and numeric output. These tools are powerful, but daunting to use correctly. To address this, I created an application called PropView "wraps" these engines: in response to your selecting a location, PropView graphically displays all band openings between your QTH and that location over a 24-hour interval; a typical screenshot is shown inhttp://www.dxlabsuite.com/propview/PropViewBands.jpg
You can optionally display a bit more information, visualizing the ionspheric properties that are responsble for the predicted openings:http://www.dxlabsuite.com/propview/propview.jpg
PropView is a member of the freeware DXLab Suite, and interoperates with other members of that Suite - like DXView. By itself, PropView lets you select a location by typing in a latitude and longitude. But if DXView is running, you can select a location by typing in a prefix or callsign (e.g. KH6 or 7O1DX), or you can select a location by simply clicking it on DXView's World Map.
PropView can also monitor the continously operating beacons on the 20m, 17m, 15m, 12m, and 10m bands operated by the International Amateur Radio Union and the Northern California DX Club:http://www.ncdxf.org/Beacons.html
With DXLab's rig control component (Commander) running, PropView lets you specify a set of beacon locations and frequencies ,and then continuously QSYs your transceiver to monitor the locations and frequencies you selected. Within 5 minutes, you'll have a good idea what's open to where (unless you have a beam to rotate, in which case it might a little longer).
While PropView and the other members of the DXLab Suite are easy to install and use (the VOACAP, ICEPAC, and IONCAP engines are automatically installed and run for you), you'll get a lot more out of them by first learning the basics of HF propagation. Appropriately educated and armed, you'll be able to exploit band openings long before the spot-chasing hordes discover them.
DX spots are quite helpful in determining when and where a needed DX station might be QRV, but if you wait until the station is actually spotted to initate your chase, you'll likely be up against a fierce pileup full of aggressive and desperate competitors; unless you have a great station or lots of patience, this can consume some serious stomach lining.
There's nothing like hearing your callsign come back from a needed DX station via a long path opening that you identified and staked out, and then completing the QSO without a lot of QRM from other callers.
PropView and the other applications mentioned above are all available viawww.dxlabsuite.com
They're all free.