Backing up Macbook with WD Passport?

I have an old backup of my Macbook on a 500GB WD Passport (which was my very first time backing up and was done for me by a Mac Genius at the store). When I try to update my current backup, the Time Machine says it has "failed" because "the backup volume can't be found". I think it is trying to backup the entire system, and not just the changes. How do I make a current backup? Must I format the external hard drive and start with a fresh backup? If so, how do I go about that?
Also, Time Machine is saying that there are only 30.7GB out of 148.7GB available. I don't understand this because the Passport is supposed to be 500GB. Again, a Mac genius at the store did my original and only backup thus far, so I am totally clueless.
HELP please! Thank you in advance.

Just use Disk Utility to first erase the drive. Make sure there is only one partition on the drive. If there's more than one, remove it and make the drive as one partition. Format the drive as Mac OS Extended Journaled, GUID scheme. After that, identify the drive to Time Machine and start over.

Thank you! How do I check if there is more than one partition (I am almost sure there is more than one)? Also, how do I make it one partition?
As far as "identifying the drive to the Time Machine", will I be prompted for that when I plug it back in after formatting?
Sorry, I am totally clueless when it comes to this stuff.
THANK YOUUUU so much!!

Just click on the "Partition" tab from Disk Utility. If you see more than one partition, highlight it first. Then click on the small minus (-) button on the bottom of the dialog. Press "apply". That will remove the partition. Then grab the partition border line with your mouse and drag it until it encompasses the entire drive. Press "apply" again.

Format the drive (see my first post). At the same time, you can name the drive - such as "Time Machine Backup" or some such.

Next, open the Time Machine application. Make sure the drive is attached and mounted. Time Machine will ask for a drive and likely "see" the drive already attached and ask to use it. After that, just press "Backup Now". It may take awhile on the first backup because everything will be backed up.

Thank you so much. Your instructions worked perfectly! I really appreciate your help.