Follow the instructions from Foursquare for exporting your data, under the question "How can I export or download my data from City Guide?".
You can export from the Foursquare website or the Swarm app, the data is the same.
Once you start the process, you'll get an email like this:
Then in 1-7 days, depending on the size of your data, you should receive an email with your data file saved as a zip file.