You've got a bit of work to do.  And, your final target should be 4.9.2.  There will be a 4.9.3 in the next few weeks, too.

First, make backups and verify them.  Second, make backups at every stage.  You will be doing this in several steps.

You will want to do some research to figure out which versions you will use.  I would start over at Mitchel Sellers' blog (mitchelsellers.com) and review his detailed upgrade instructions.  I don't recall if he goes back to 3.0.1.

Starting with 3.0.1, you will want to upgrade to a version of 3.x that has a 4.x counterpart.  You can figure that one out looking at the dates of the releases.  So ... upgrade to a version of 3.x, and then upgrade that to the 4.x counterpart.

Check this out and make backups.

Once you get to 4.x, I believe that you can try upgrading to 4.6.2.

Both of those upgrades will require that you update the upgrade web.config file manually.  That is why you need backups -- if you miss something, you will need to restore the database and web directory to try again.

Once you get to 4.6.2, I believe that you can upgrade directly to 4.9.2 or 4.9.3 (if it is available).  This upgrade doesn't require fiddling with web.config.  It will be a snap.

Your biggest problem may be modules, particularly if you use custom or third-party modules.  Before you start, you probably will want to check to make sure that all of your modules will work.  Where there are issues, you'll need to look at replacements.

If you have questions about any specific step, please keep asking questions.

You may want to read this:

How to Upgrade DotNetNuke v3.x to v4.4.1

How to upgrade DotNetNuke from v3.x to v3.2 on a live website

and then

• How to Upgrade DotNetNuke (Auto Merge Method) (v4.6.2 to v5+)
• How to Upgrade DotNetNuke (Manual Method) (all versions)