On an Android-based or iOS-based mobile device, you can use special formed URLs in order to start the Foursquare application viewing the desired venue: https://developer.foursquare.com/resources/client
The URL https://m.foursquare.com/venue/#venue_id# (e.g. https://m.foursquare.com/venue/4b477346f964a520723226e3) can either be opened by the installed Android Foursquare App or opened by a normal browser (or other Intent receivers registered for that URL).
You can further use the URL https://foursquare.com/mobile/checkin?vid=#venue_id# to get to the mobile page, where you can just press "check in" or enter a shout. By checking-in via the mobile page (and not the app), you do not get points and are not able to earn Mayorships (see Foursquare support).
But you can, for example, create your own web app that accesses the Foursquare API and performs the check-in for the OAuth'ed users. By using the HTML5 Geolocation feature, you can also send the mobile device's Lat/Lon coordinates to your web app and perform valid check-ins that also count for Mayorships, etc. A good start is Foursquare's developer page: https://developer.foursquare.com/overview/