There are two ways to get your apps onto the 6310i.
The first is using downloading it using the WAP browser. This requires you to have access to an internet connected web (wap) server. You simple put the file on the server, create a small piece of WML that links to the JAR file and access this with the WAP browser of the phone. Select the link the the MIDlet will download to the phone.
The second way is to download the Nokia J2ME Developers Suite Beta 0.3 and connect your 6310i to your PC with the data cable. The Developers Suite supports deploying MIDlets directly to a 6310i device. It's also supposed to support an IR connection too, although I've never managed to get this working.
The PC Suite version 4.81 is now available for download on the Nokia site and this version includes the Application Installer (4.80 does not). Remember to uninstall the previous version. With the application installer you can download .jad and .jar midlets from the web and install them directly to your phone.