Travel information to take note of
Although you may be coming from another Shengen Zone country you will be asked to produce a valid id card or passport when entering Sweden.
How to get to Lund by plane
The closest international airport is Copenhagen airport (CPH). There are direct trains from the airport to Lund every twenty minutes and the trip takes about 1 hour. Before boarding the train at the airport you have to go through an id-controll and show your passport. When the train comes to the first stop in Sweden called Hyllie it stops for a border-control. You can stay on the train but you will have to show your passport again. Then the train proceeds to Malmö central station (via a station called Triangeln) where it stops for up to 20 minutes in order to be in sync with the timetable. After that it will continue to Lund, so again you can stay on the train.
An alternative is the regional Malmö/Sturup airport (MMX) which has a few international flights. There are airport buses to Lund approximately every hour.
More information can be found at this link:
How to reach Lund by train
Lund Central Station is connected to Swedish stations and to European stations. More information can be found at this link: http://www.lunduniversity.lu.se/about/visit-lund-university
You can take a train (one called "Öresundståg") from Copenhagen airport directly to Lund central station. Then city bus nr. 6 towards "Östra Linero" and get off at "Sparta". The bus leaves from bus stop "K" at the train station.
Google map link: https://goo.gl/maps/Bz8hufbEgHA2
Time tables can easily be found at https://www.skanetrafiken.se/sok-resa/ which can be translated to English from the button in the top right corner. Tickets can be bought with credit card (VISA, VISA Electron, MasterCard and Maestro) in Skånetrafikens ticket machines outside the arrival hall at the airport. It is not possible to buy tickets on the train (or the bus), so one has to do it before. Otherwise you be might charged an extra 100€ control fee. The ticket will be valid within Lund, so you don't have to buy an extra for the bus. There are several different types of ticket machine at the airport, you need this one: