1. Download the Tekkit server 3.1.2 and unzip it.
2. Grab an FTP client and connect to your server. (There are instructions on how to do this on the beastnode support site and even a recommended FTP client. You can get your FTP connect info in the Multicraft CP under Your Server > Files > FTP File Access.)
3. Upload all the unzipped files and folder to the root of your server. (You can skip uploading launch.bat and launch.sh, you won't need them.)
4. Create a "jar" folder in the root of your server.
5. Move Tekkit.jar into the jar folder.
6. Close the FTP client.
7. Log into the Multicraft Panel for your server.
8. Open your server in the cp.
9. Save-all and stop the server, if it's running.
9. Under "JAR file" type Tekkit.jar, click Save.
10. Start the server.
I use BeastNode as my host also but it's been a few weeks since I set mine up so I think this is all the steps. Check the console for error messages after you start it up. You will want to create a new map to get access to all the new ores and gemstones in Tekkit (unless you have an existing Tekkit-created map). If this doesn't work or you need more help you may need to submit a ticket to BeastNode. You can post questions here but I don't frequent these forums so I may not respond.