Anyone who uses an LMH1251 to drive a 75ohm input directly is an idiot. If they're DC coupling it, doubly so. The datasheet specifically says not to do it, and the outputs aren't designed for it in any way, shape, or form.
There should indeed be a buffer between the 1251 and your monitor input. The LMH6739 identified in the datasheet is presumably suitable. The non-inverting input (+) is what you want to hook the outputs of the LMH1251 up to (via those caps, resistors, and clamping diodes - that all builds a DC restoration circuit). The inverting (-) input can be left unconnected since the LMH6739 has internal feedback resistors. Tie the disables high (inactive), and apply a clean power supply between Vs+ and Vs-. Outputs then go to your monitor via the 75 ohm resistors (which is the back termination for the monitor input).
If you're new to things like this, I'd try a simpler project first since high bandwidth op-amps can be tricky to work with. Most of them are only available in surface mount, and they'll tend to oscillate if you're not careful with the layout due to the parasitics introduced. You can certainly give it a shot, though. National will probably sample you an LMH6739 or two for free (they'll even pay the shipping).