Before you start

Established UK residence
Your foreign licence
A UK address for the DVLA
Proof of identity, usually your passport and eVisa share code

Step-by-step

1
Consider not driving at all
Edinburgh's centre is medieval, the parking is permit-controlled and expensive, and the city has a low emission zone. Lothian Buses is one of the best municipal bus networks in Britain and the tram now runs from the airport through the centre to Newhaven. Car ownership here is a choice most people decline.
OnlineWho: You
2
Check whether your country is a designated country
The DVLA maintains a list of countries whose licences can be exchanged without taking a test, within five years of becoming resident. If yours is on it the process is a form; if not, you face the full UK theory and practical tests. Check before assuming.
OnlineWho: YouBefore the deadline expires
3
Act within the permitted window
You can generally drive on a valid foreign licence for twelve months after becoming resident. Designated-country exchanges must be made within five years of becoming resident. Missing either window costs you options.
OnlineWho: You
4
Apply to the DVLA by post or online
Exchange applications go to the DVLA in Swansea with your foreign licence, which is retained. Processing takes weeks, and you will be without the original in the meantime.
OnlineWho: You
5
If you must test, budget properly
The UK practical test has long waiting lists and a low first-time pass rate, and lessons are expensive. Someone from a non-designated country should start early rather than assuming it is a formality.
In personWho: You
6
Understand the low emission zone
Edinburgh operates a low emission zone covering the city centre, with penalties for non-compliant vehicles. Check any car against the standard before buying, and check the zone boundary before driving in.
OnlineWho: You

Documents you’ll need

Foreign driving licence
Passport and eVisa share code
Proof of UK address
DVLA application form appropriate to your licence's origin

Things most newcomers don’t know

The 'designated country' list is the whole question, and people assume rather than check.

If your licence was issued by a designated country you exchange it with a form and a fee, within five years of becoming resident. If not, you take the full UK theory and practical tests regardless of decades of experience. The list is specific and includes some countries people expect and excludes others. Ten minutes on the DVLA site saves either an unnecessary test or a very unpleasant surprise.

Source: GOV.UK — exchange a foreign driving licence

Edinburgh is genuinely a city not to drive in.

A medieval street plan, extensive permit parking, a low emission zone, and one of the best bus networks in Britain plus a tram from the airport to the coast. Adding a hill that the Old Town is built on top of. Most residents manage entirely without a car, and visitors who bring one spend the week regretting it.

Source: community-reported

You have twelve months to drive on a foreign licence, then it stops.

After becoming resident you may generally drive on your existing licence for twelve months. After that you need a GB licence, whether by exchange or by test. People drive for years on a home licence without realising it stopped being valid, which is a serious problem after an accident.

Source: GOV.UK — driving in Great Britain on a non-GB licence

Scottish banknotes are legal but occasionally refused in England.

Notes issued by the Bank of Scotland, RBS and Clydesdale are legal currency in Scotland and are not legal tender anywhere — a technical distinction that means English retailers can refuse them, and sometimes do. Keep some Bank of England notes if you travel south regularly.

Source: Bank of England