For basic soldering techniques/procedures, take a look at the following:
Soldering Procedures (text w/ illustrations, printable)
Pace's Soldering Tutorials 1 - 9 (youtube videos).
These will take time, but well worth it IMHO.
Plenty of others out there as well, but I'd recommend starting with these, as it will help you distinguish between good and bad practices you might encounter in other videos.
Couple of questions:
Quick question, what do you currently have for an iron, supplies (i.e. solder wire, flux, wick), and skills?
Can you post some more pics of the item's to be soldered (it's pins/leads, as well as the pads on the PCB)?
Not sure if there's something fine pitch or not hidden under the display (wouldn't think so), hence the request for pics for clarification (or typed will be sufficient if there's nothing there). FWIW, based on the holes alone, it won't be hard after picking up the right techniques and a bit of practice on scrap PCB's first.