In reply to An Triubhas:
Flights:
Flights go to and from Longyearbyen daily either via Tromsø or Oslo. Main carrier is SAS however Norweigan have plans in the pipeline to provide a service here. Tickets can be quite cheap, though as you're not a youth, you may find them a little more expensive, even more so if you travel full flex.
Accommodation:
Cheapest place by far is the hostels these are in Nybyen to the south of town and you'll live with the student bums. It takes a good 30min to walk into town and the uphill back, although scenic is a bitch. Second best and always the top of our list is Mary-Anns Polarrigg, cheaper than the Radisson, Svalbard Lodge or Basecamp.
Planning your trip:
http://www.toposvalbard.npolar.no this is the best on-line resource for mapping, almost all of the shops, the museum and hotels sell maps so you will certainly be able to get hold of one when you get there.
Do you have any idea of where you would actually like to go and when?
Law:
Svalbard is different and they uphold the law to shit. Much of the area around Longyearbyen is a free for all. The rest is a nature reserve where you are required a special permit to have access to. Any expeditions outside management zone 10 are also required to have notification and pretty damn good insurance provided to the Governor before you will be allowed to go. Don't try and avoid this, they fly regular spot checks and will fine the hell out of you if caught.
Start here:
http://sysselmannen.no/en/Visitors/Planning-a-trip/
http://sysselmannen.no/Documents/Sysselmannen_dok/Kart/Svalbard_forvalt_10....
Rifles aren't actually law (yet) outside of inhabited areas it's a recommended precaution. However once you get one (from basecam, sports senteret, wherever) go and learn how to use it. Chances are you arent that familiar with a K98F, Ruger M77 or a Sig/HK/rustyww2pieceofshit flare gun.
see:
http://sysselmannen.no/en/Shortcuts/Firearms-/Renting-firearms/
Other stuff that's nice to consider is the nature you're in, you are expected to act and behave in a responsible way and if not the consequences can be pretty damn harsh
Equipment Hire:
Most of the guiding offices (Basecamp, Spitsbergen Travel, Svalbard Wildlife etc...) will have a hire service. But tbf just get friendly to a local and chances are you'll be able to borrow quite a bit
Kit:
To help here it is best to know when you're going. Winter is almost pointless, its dark, scooter season hasn't started and you wont see a thing. The most popular times are spring and summer. The climate is relatively stable throughout and the worst of the weather comes with the wind.
Spring is Snowmobile, ski-pulk and snowshoe time. It's also the most popular period for people getting out there and chances are you wont be that far away from someone.
Even in summer it can be bloody cold, but equally as predictable, central Spitsbergen is pretty moody, so you need to be prepared for all kinds of weather. However standard UK winter clothing and system hasn't let me down thus far.
Camp Safety and other essentials:
This is a biggie and I mean you need to be freakin' switched on:
Satellite phone: you need one, no matter what this is the single most important piece of kit you can have (they can be hired). Set up a call in time wherever in the world, 30secs just to let people know you're alive. The guides may even be your service, where they can provide a weather report too and also have a good idea of where you are should something go wrong. Second to that is an emergency beacon, also available to hire iirc.
Camp safety, starts with shit hot admin, no food in the tents and either well packed a good 40m or so away (we say 50 but normally it's about 10) in a metal (zarges) box or some-such. Keep your toilet even further away and ideally down-wind of you. Set flares (properly, learn how to do this) around your camp about c.4m away from the tent on all sides. Mark the wire so you don't trip it in you're dreary I need a piss induced sleepwalk. Sleep with a 'half loaded' (the term amuses me too) rifle between you, the flare-gun by the tent entrance and keep something hefty close to hand. Polar bears hunt seals in winter by smashing through their dens after hearing the breathing... when you're snoring and wrapped up in a sleeping bag, you look and sound a f*ck load like a phat seal to a bear.