Changing a Remington barrel is not for the casual DIYer - it should be done by either a professional gunsmith or an advanced hobbyist. Depending on what type barrel you're using, it may be essentially plug-n-play, or it may not. A factory take-off barrel may screw right on and head space properly; then again, it may not. An aftermarket barrel will need to be threaded, have the bolt counterbore cut, and be chambered. A dedicated barrel vise and action wrench are required to remove and install rifle barrels. A lathe is needed to thread and chamber (well, actually you can chamber without a lathe).
Your bolt would need to have the face opened up to accept the much larger magnum case head of the .300 Win Mag.
Check around with a good local gunsmith to see what he would charge for this work. Many barrel makers will install your barrel; a few won't.
