That is a fairly advanced repair if you are new to it all.
Ideally you would have hot air for this but you could do it with a more conventional iron if you have to.
Either way you will probably want solder braid/solder wick for this (and some flux). I have seen such things done with a solder sucker but you are making it harder.
Remove the balls at the end and it should free most of it, or at least enough to get the rest. As it is likely to be lead free then you might want to flow a bit more of some nice leaded solder on there to make life easier.
Replacing after that is basically the reverse of that. In an ideal world you would use a stencil and solder paste but that is within reason for a normal iron and drag methods (the green stuff on top of the PCB won't take solder so dragging it away from the connector will work), or hot air. If you wanted some solder paste and to apply it with a needle then that would also be easier.
Some will also tack it down with a bit of super glue before they solder, or maybe some other type of glue. At precisions like this I can go either way and maybe hold it down with a toothpick/cocktail stick or something.
As far as replacement sockets... always fun and that is even if you can find them on the usual suspects for parts (electronics vendors** will stock such things, wait until you see their shipping costs/minimum orders).
You can try looking for a repair kit online to see if someone put one together (sometimes people will) but it is not normally what we see on the failures front so I doubt it -- such things tend to be more "here is a collection of the capacitors/resistors/other passives that fail all sized and in one pack for your convenience".
You might find a broken motherboard and attempt to recover them but that could be easier said than done, to say nothing of cost (or whether you just chuck that motherboard in instead).
*electronics companies list from my bookmarks, some probably dead (the maplin link being put there later on and still years before they died on the high street) but eh
http://cpc.farnell.com/
http://www.element14.com/community/index.jspa
http://www.jaycar.co.uk/
http://uk.mouser.com/Home.aspx
http://www.rapidonline.com/
http://www.anglia.com/product_search/product_search/index.asp
http://uk.farnell.com/
http://uk.rs-online.com/web/
http://www.digikey.co.uk/
http://uk.futureelectronics.com/en/Pages/index.aspx?OL=GB&Language=en-GB
http://www.sparkfun.com/
http://www.maplin.co.uk/
http://www.scan.co.uk/
http://www.ownta.com/
http://www.virtualvillage.co.uk/
http://proto-pic.co.uk/
http://www.pamir.com/
http://bitsbox.co.uk/
http://www.jameco.com/webapp/wcs/st...splay?langId=-1&storeId=10001&catalogId=10001
http://octopart.com/
http://www.findchips.com/
http://ebluar.com/
http://discoazul.co.uk/
http://www.coolcomponents.co.uk/catalog/index.php?cPath=50_74
specific parts and guides
What ones you pick as far as replacements is more about it fitting within the footprint, same number of pins (technically you could do more but it makes life harder), pins on the correct side (no point in having ones with the pins coming from above unless you want to invert the ribbon and all the tracks... which you don't) and having the same pitch** between the tracks/pins (they are usually one of a series of different sizes rather than completely custom but still enough that it might be a fraction of a mm out and thus potentially short, though if it is only 4 pins you might get lucky and be able to twist it slightly to have it all line up if it is bigger).
ZIF is short for zero insertion force and is just another way of doing it that some like. They come in various forms depending upon what is being done. If you find one that is suitable then great, otherwise if you can then do go for like for like unless you want to argue a case otherwise (I have replaced connectors on things that were ill chosen in the first place).
**if you want to get really crazy you can sit it on an insulator to stop things shorting and run wires down to the original pads. That is however normally the sort of thing I reserve for "this device runs my factory, every hour I am down costs me probably more than your year's wages" or "we are deep in the heart of somewhere unpleasant and this will allow us to call for a plane/complete the job" type scenarios. Given even the rip off merchants at CEX will sell me a whole one for £100 then... yeah.
Cowboy method of fixing. You could run wires from the solder joints at the back (or some other suitable location) of those to their respective pads on the ribbons. If you are going to do this I would suggest you find some old ribbon cable from a computer and use that (IDE cables are wonderful for this but most such things will do).
