The only airport in the region is Glasgow Prestwick International Airport (PIK), which is primarily a destination for a number of low-cost airlines. Prestwick airport can be reached directly from European cities including Brussels, Dublin, Frankfurt, London, Milan, Oslo, Paris, Rome and Stockholm. The airport has its own railway station, with direct links to Glasgow Central Station (a 45 minute journey) and to Ayr (7 minutes). See below for further information. Ryanair passengers can get a discount by showing their flight paperwork to the ticket inspector when you purchase on the train.
Glasgow Prestwick International Airport  - Airport information and live flight times.
Ryanair  - Online ticket sales for flights to/from over 15 European cities.
Like most of the central belt, the south west is well served by Strathclyde Passenger Transport, with train stations in most towns. There tend to be two trains per hour on most routes, though be sure to check ahead, especially on holidays and Sundays where there may be scheduled engineering work.
Most places here can be reached via Glasgow Central station, with a journey down to Ayr taking about 55 minutes and costing around £7 return. Glasgow to Stranraer typically takes 2 hours and 15 minutes, costing £16. From England, trains tend to head straight into Glasgow Central, though there are routes leading to Kilmarnock, from where more local destinations can be reached.
Tickets should be purchased at stations where available, but can be bought on board too. Single day return tickets generally cost very little more than a single ticket and so you should buy a return ticket if you'll be travelling back on the same day. Purchasing a "Daytripper" ticket from any station (£15 for a family of four) allows virtually unlimited travel across the Strathclyde network of trains, buses and the Glasgow subway for one day. Bicycles are accommodated freely on most train journeys, though space is not guaranteed.
Strathclyde Passenger Transport  - Route maps and ticket offer information.
First ScotRail  - Timetables and online ticket sales for journeys across Britain.
Being near Northern Ireland, there are a number of ferry routes into the south west of Scotland. SeaCat operates a ferry service between Belfast and Troon. There are typically at least two sailings a day and a single passenger ticket costs from around £30 to £40, depending on the time of year. Taking a car on the ferry costs from £85, again depending on the time of year and ticket type.
The other ferry operators listed below appear to have cheaper prices, so check all of the websites before booking.
SeaCat  - Ferry timetables and ticket sales from Belfast to Troon.
Robert Burns, the famous poet, was born in and has many links to the the region, so there are a number of attractions to see, many of which are in the Burns National Heritage Park  in Alloway, Ayr and his later home Dumfries.
The region is famed for its numerous golf courses (over 60). Indeed, the first Open Championship was held at Old Prestwick in 1860, with Royal Troon hosting the 2004 tournament.