I got the bright idea that I would "fine tune' the front derailleur on my wife's Haro Vector mountain bike. Alas I am apparently not naturally gifted at this task. If someone could please instruct me on the proper way to get this back to functioning, I would greatly appreciate it. I've managed to get it to skip from small to large sprocket and completely skip the middle. It has index shifting and I am woefully out of my league. I'd like to safe the 50 bucks at the bike shop and consider myself mechanically inclined but I am clearly missing a nuance somewhere.

Try the Park website and use it step by step and you should be OK.
https://www.parktool.com/blog/repair-...ur-adjustments

Follow the Park Tool procedure above. Start at the beginning and do not skip any steps as each one depends on the previous steps being done correctly. Make the adjustments in small increments, 1/4 turn or less, so that you do not overshoot the adjustment.

I appreciate that but there's so much reading and technical jargon it makes my head hurt. I'm not one to shy away from my own research and learning but I was more looking for general tips to steer me correctly. This particular bike clamps around the town tube so I can adjust up and down but side to side, not so much. I get the high/low concept but the turning of the screws does not seem to have the desired effect.

If you are going to work on bikes, you will need to learn some of the jargon like we all do. I use the Park book so I can have it right there where the bike is and look and read and look. Look to see if your high/low screws are actually touching anything. If they are, adjusting them will make a difference. The first time can be confusing but each time gets easier, though I still use the book to get the order of adjustments correct. Keep at it, you'll get it.

Uh, you're skipping way too many steps. Go back and read through the Park Tool site until you're familiar with all the jargon and understand the procedures. IF you follow that Park Tool - Front Derailleur guide posted, and do each and every step listed to the specifications listed, our front-derailleur will work magically!

BTW - the high/low limit screws do nothing for shifting performance. They are an insurance-policy against overshifting to the inside or outside. But until your chain has shifted from one ring to the other, the limit-screws don't even come into play. They will not improve your shifting from the big-ring to the small-ring, nor will they help shifting from the small-ring to the big-ring. Don't focus on the screws until the very end, when your chain is shifting so well between the rings, that it keeps on going and falls off on the inside or outside.

That is by far the most eye opening advice I have gotten! Thank you very much. There is no magic bullet and I guess I better get to the park tools site and hammer it out. Thanks everyone.