Here's how I do it:
1) back up all files on the current 4.4.1 install (I copy all into a zip archive).
2) back up the database.
3) in best of all possible worlds I then download these to a development server, create a database, and restore the 4.4.1 database over it; then extract the files, create a virtual directory, change the connection string to point to the new database, and after creating a user on the database that has dbo privs, put that user in the connectionstring.
Now you've got an exact copy of your 4.4.1 install which you can upgrade to 4.5.3
1) use the Upgrade version of DNN 4.5.3 ... unzip the package right over the files in your local 4.4.1 website. Now compare the new release.config file with your current web.config file ... make a backup copy of your web.config file first ... and update the web.config file to include the new features in 4.5.3 but set as you want them.
2) navigate to your local website and the upgrade should happen automatically. Take notes on any/all errors if you encounter any. If all the above has gone ok, you shouldn't expect any.
You could skip doing this locally, of course, and just do it on your production instance; but making sure you have backed up both file system and database first is crucial. Comparing web.config and release.config so you have a web.config files that both includes new stuff from release.config but retains old stuff from your web.config (connection strings, machine keys) is always necessary.
To upgrade on the production server, I upload the upgrade zip file to the portal root directory by whatever means (ftp or via hosting control panel) and in the hosting control panel I then unzip the file, which then overwrites the core parts of the file system ... sometimes I do the web.config / release.config editing prior to uploading, and pull the web.config into the upgrade zip file, so it's ready to go - easier than editing online.
If all goes well, you have an upgrade. If things crash around you, you have the database backup and the filesystem backup and can return to the way the site was before you made the upgrade attempt; you'd delete all the files, unzip your old filesystem, and restore the database backup over the database to return it to its previous state.
There are far more complete descriptions, step by step, on performing this task, and I suggest you check some of them out; I'm painting with a somewhat broad brush, but it might be enough for you to succeed anyway. You'll want to become familiar with this process if you will be using DNN and upgrading from time to time.
I have no idea how the wizard would play into all of this - I don't use it for installs or upgrades as I prefer to keep my hands on the wheel; have done this enough that I'm comfortable with it and prefer the familar territory.
At any rate, think it out ahead of time, understand what you are doing, and prepare for the possibility that things could go wrong. If they do, releax, go slow, and don't make any decisions in a panic!
If this is your first time, absolutely do it locally a couple of times first - install a 4.4.1 DNN instance, and upgrade it to 4.5.3 ... and then roll it back to 4.4.1 ... you want to make sure you are comfortable going both directions. Take decent notes and when you've done both the upgrade and the rollback successfully at least two times ... then you will find that you can do it again (in both directions) in a matter of minutes. So do it again ... a third time, both ways .... why not? Having that experience and confidence is irreplacable regardless of how many tutorials you read!
Then when you go to do it in production, you'll have a real sense of what you are doing that will both help to avoid problems, and respond rationally and successfully when the unexpected problem does arise.