There are two airports close to Lund: Malmö Airport (Sturup) located 30 km south-east of Lund and Copenhagen Airport (Kastrup, Denmark) about 25 km south-west of Lund.
Kastrup (CPH), Copenhagen Airport, Denmark to Lund C
As you will see from the air, Kastrup is next to the bridge to Sweden. From Kastrup trains across the bridge to Sweden (Öresundstågen) leave from platform 1 at least every 20 minutes (at 1:00-5:00 at night ones an hour) to Malmö C. Some of the trains continue to Lund C, but it might be that you have to change train in Malmö (purple commuter trains called Pågatågen). From the airport to Lund, the travel time is about 35 minutes. A one-way ticket (ask for a ticket to Lund) is approximately 110 DKK or 135 SEK and are sold at the ticket counters before going down the conveyor belt down to the trains. Most credit cards are also accepted.
Sturup (MMX), Malmö Airport, Sweden to Lund C From Sturup, there is a bus (Flygbussarna) to the centre of Lund (approximately twice an hour). A one-way ticket, bought on the bus, is 90 SEK . A 30 minutes taxi ride into Lund is about 250 SEK, but be sure to ask for the price before you take the taxi. There are unfortunately some non-serious drivers. Most taxis accepts credit cards (sometimes for a minor additional fee).
The train station in Lund (Lund C) is located in the centre of Lund. To continue here you can walk, take a bus or get a taxi.
Bus from Malmö
Note: Not from Central Station - take train instead
In addition to the above, for people going from and to Malmö City (Södervärn and Värnhemstorget) there is also the option of taking the commuter bus Pendeln 171 (Malmö Södervärn - Malmö Värnhem - Kårhuset/LTH - Lund University Hospital and return) directly to LTH. The bus takes 20-25 minutes and runs about every 5-10 minutes in weekday rush hours and once an hour on Saturdays.
Source: Skånetrafiken http://www.skanetrafiken.se
Bus from other cities in the region
For buses to and from other cities see Skånetrafiken link above.
There are a few different ways to get from the train station (Lund C).
Walk: To walk from the train station takes about 20 minutes. City map.
Bus: For all buses below, get on at bus stop K which is located at Clementstorget (on the north end of Lund C). The trip will take less than 10 minutes.
There are also other busses going between the station and LTH. For more information and exact times consult: http://www.skanetrafiken.se/ (departure from "Lund C" and arrival at "LTH").
Taxi: Ask for: