Most countries from which GUADEC attendees come do not require a visa to visit the UK.
UKvisas gives information for each country, including the information that needs to be provided to apply for a visa, and where it should be sent.
A UK 'visitor' visa is sufficient to attend a conference: you do not need a business visa.
Note that the UK is not a Schengen country: Passports (or identity cards for those countries that issue them) are checked even when arriving from elsewhere in the EU.
If you need a visa invitation letter, please fill out the request form, giving details of your full name, passport number and job title.
The nearest airport is Birmingham International, about 6 miles out of town however there is a train station on-site which takes you to Birmingham New Street for a few pounds. It is well served by a mixture of charter, scheduled and budget airlines from across Europe.
For those flying from outside of Europe there are two alternatives:
For those arriving from within Europe from destinations not served by Birmingham International then the next closest airport is East Midlands.
Birmingham New Street train station is at the centre of Birmingham, and has links via to the Birmingham International via Birmingham International Interchange.
Due to the complexity of the train network it will be easiest if you look up the appropriate service for yourself. One of the best sites to do this is www.traintimes.org.uk which provides an accessible version of the www.nationalrail.co.uk timetable service.
It's easy to get to the Conservatoire by foot from the station: 1 mile trip
M6 J6, come up the express way with the electronic sign posts ahead and I think it's the 2nd exit on the left (sign posted for the Jewellery Quarter) just before the entrance to the tunnel, you go up a steep hill and the venue is in the middle of that roundabout. If you go all the way around and take a left at the hotel you'll find an NCP car park opposite the venue on the other side that you approached. Somebody else can probably explain that better.
National Express provides the largest coverage across the UK.