Pre-travel preparations:
Travelling on an exchange to Leiden was extremely fun and rewarding and I strongly recommend going if you have the chance. Before you travel though, there are several things that you need to be arranged which at first may seem like quite a hassle, but once you get started everything really goes quite smoothly. The International Coordinator at KI is always willing to help and usually knows what needs to be done if you don't. Below I have written down some of the most important things to think about:
Applying:
The first step is of course to apply for the exchange at KI. Once you have become nominated for the exchange an application must also be sent directly to Leiden University. This is done online at:
https://www.apply.leiden.edu/exchange-studyabroad/Index.php and is rather straight forward.
A few weeks after you have applied you will receive an Acceptance of Admission via mail. This needs to be printed, signed and then sent back to Leiden in order to accept your place at the University.
Accommodation:
When this is done it is good to start looking for accommodation as soon as possible. Like many other University towns, a lot of exchange students come to Leiden and there is usually a lot of competition for housing in late August/early September so start looking early! Leiden University provides their own student-housing service, but it is quite expensive (difficult to get a room for less than 500 €).
A good idea is to ask the international coordinator at KI for help, as there are usually several students from Leiden coming to study at KI that have rooms or apartments in Leiden that they want to rent during their time in Sweden. I got my room this way, which saved me a lot of trouble looking for accommodation and gave me a room for a decent price (350 € per month).
If there are no rooms available this way a good place to look for accommodation is Leiden Housing on Facebook: https://www.facebook.com/groups/239427083843/
Flight tickets:
Booking a flight ticket is also something that is best done early. Several airlines fly directly to Amsterdam (Schiphol) from Arlanda among them Norwegian, which have reasonably priced tickets:
http://www.norwegian.no/
Other:
In addition to this you should sign up for the orientation week (not sure if it's mandatory, but it's definitely something you don't want to miss!) and print and fill in your arrival form (can be found here: http://media.leidenuniv.nl/legacy/arrival-form-visitors-centre-sea.pdf).
You should also remember to get a European Health Insurance Card at http://www.forsakringskassan.se/privatpers/utomlands/eukort , make sure that your passport is valid and that you have applied for funds from CSN.
Finally, check out KI's and Leiden University's websites regarding going on exchange to see if there are any additional things that are required from you.
KI:
http://pingpong.ki.se/public/courseId/7085/coursePath/5549/ecp/lang-sv/publicPage.do?item=3923702
Leiden Uni:
http://www.prospectivestudents.leiden.edu/study-abroad-exchange