Transfer from old hosting to new hosting

Hello, i recently went from Hosting24 to Ssdapp and while ssdapp as helpful in setting up the VPS and installing webmin etc, they lack the expertise to transfer the website from old to new, and i personally have no idea how to do it. So any help transferring would be great, currently it's an IPboard site, and i have nothing set up on the new VPS Ssdapp said it should only cost around $10-15 for transfer so i'm hoping to keep it around that.