Flight connections:

The closest airport with good bus connection is Basel/Mulhouse (CH/F), cheap airline are www.easyjet.com, besides many others.
Important: Leave the airport buidling through the French exit, there is a direct bus to Freiburg/Breisgau main station. The bus leaves every 90 min, and takes 60 min to Freiburg. Bus information under: www.freiburger-reisedienst.de (Airport Bus), or telephone: 0049 -(0)761 - 500 500
Airport info: www.euroairport.com

Frankfurt is ist the most important and nearest international airport, about 2,5 h by fast train (ICE). Many international airlines serve this airport. There are direct trains from the airport (Frankfurt Flughafen) to Freiburg/Breisgau main station every hour. See www.bahn.de.
Airport info: www.frankfurt-airport.com.

Frankfurt/Hahn has cheap airlines (www.ryanair.com, www.wizzair.com), but is ca. 1h by bus away from Frankfurt airport and the train connection (plus another 2,5h to Freiburg). Therefore it needs time, but you have many cheap options inside Europe!
Airport info: www.hahn-airport.de

Baden Airport (~ 1,5 h away from Freiburg/Breisgau). Small airport with a few cheap flights www.ryanair.com/www.airberlin.de. (For the flights from London there is a direct bus to Freiburg only on work days). Another option is to take a bus to Baden-Baden main station and then the train to Freiburg.  Trains: www.bahn.de. The "Baden-Württemberg-Ticket" might be interesting if you are more than 1 person traveling (see below travel by train!)
Airport info: www.badenairpark.de

Airport Stuttgart is about 2,5h from Freiburg/Breisgau. Here you take the S-Bahn (every 10 min) to the main station and then the ICE train to Freiburg. (www.bahn.de). The "Baden-Württemberg-Ticket" might be interesting if you are more than 1 person traveling (see below travel by train!) Cheap airlines check www.germanwings.com besides many other airlines.
Airport info: www.flughafen-stuttgart.de

Strassburg (France) is close but takes a minimum 2h to Freiburg/Breisgau. You have to take a bus to the main station and then take a train to Freiburg. This train connection is not well developed, see www.bahn.de. The "Baden-Württemberg-Ticket" might be interesting if you are more than 1 person traveling (see below travel by train!) Valid from Kehl on!
Airport info: www.strasbourg.aerport.fr

Zürich (CH) is as well an important international airport, 2,5 h by train. The airport has a train connection to the Zurück main station (every 10 min). Trains to Freiburg/Breisgau over Basel. There are trains almost every hour, see www.sbb.ch.
Airport info: www.zurich-airport.com

Airport München is about 4,5 h by train! Take first the bus to the main station and then the ICE to Freiburg/Breisgau via Karlsruhe, see www.bahn.de. This is really far, we do not propose this one!
Airport info: www.munich-airport.de

For guest from Ukraine (Kiev):
www.wizzair.com offers a very cheap flight to Memmingen that is located between Munich and Stuttgart and not well connected. You have to take a but to the train station and can use the quicker train connection viea Stuttgart www.bahn.de. The "Baden-Württemberg-Ticket" might be interesting if you are more than 1 person traveling (see below travel by train!) But this tickes is not valid directly from Memmingen but from the next city direction Rabensburg or Biberach, ask at the train station in Memmingen if you are interested! You will need to change trains several times!

Travel by train:

You get all information and connections on www.bahn.de and can book via internet.

They have now cheap train tickets from different european countries (Also from London!). See the site - Europa Spezial. You need to be fast with booking!

For cheap tickets check “Offers for Travelers in Germany” and “Offers for Travelers in Europe”. There are cheap tickets for the IC/E trains (“saving fare 25” and “saving fare 50”) if you book via internet up to 3 days before leaving, only booking round trip. There is only a little amount of these cheap tickets. It’s better to book in advance, but you can only use that ticket for the train you booked.

Or “surf and rail” tickets for ICE if you book on Saturdays for the following week, only on some lines.