Ok, as I have posted in a few threads, I am relatively new to biking. I have a hybrid that I use on the local paths, some of which have a few challenging inclines. The shifters are grip shifters. The bike sat fro a few years and the cables deteriorated so I had new cables put on at the LBS. He told me I would need to come back to have them adjusted after a while. I did bring it back in after a week or so and the shifters were not changing gear properly. So now it has been a week and the shifting is worse. I attempt to go from say 5 to 6, nothing changes. At times I will go from 3 to 5, nothing. Anyway, hopefully you get my meaning. Am I doing something wrong? Is this normal for new cables or is there a possibility that my LBS is lacking in skill? It is getting more than annoying.

Probably an easy fix. The problem is more than likely cable tension, which you can fix by turning out the barrel adjusters. Follow the cable from the shifter to the derailleur. At some point you'll come to a place where one threaded little nut-looking thing goes into another. Turn the first piece counterclockwise to take up slack until it shifts right. If that doesn't help, turn the piece nearly all the way in, then go to the derailleur, loosen the nut that holds the cable, pull the slack out of it and retighten the nut. Then go back to the barrel adjuster and turn the first piece out a little as before. If THAT doesn't work, go to www.parktool.com and hunt around until you find instructions about adjusting deraillers.
I'm not sure what you mean by 5 to 6 or 3 to 5, but if can't shift to a LOWER gear (which is UP the cassette, from a small cog to a larger one), your cable has too much slack in it. The adjustments I've described should fix it.
It's common for new cables to stretch, but the repair is so ordinary that any shop should be able to deal with it in seconds. I'd take it back and ask them to give it another try, and to explain as they went. Next to fixing a flat, this may be the problem you'll encounter most frequently. It just makes no sense not to learn to do it yourself.

If the cables were corroded, shouldn't they replace the outer section also when they put new cables on? They might still be binding in there.

Pretty commonwith new cables. I've had some that are corected on the first adjustment and some that take 2 or 3 adjustments, depends on cables.

Place the shifter so that you know the position should be in the highest gear in the rear (cogs). Turn the barrel shifter til the chain starts to hit the next highest cog (you'll hear the chatter).

Then turn it back about 1/4 turn. You should be right in the ballpark of a proper adjustment. Then fine tune with a 1/8 tunrs til it runs quietly, should be right on at this point.

You don't state the "Quality" of the shifters- but on the cheaper versions fitted to most Cheap end bikes- They deteriorate very quickly. First sign is that the shifting is not crisp and missing gears. Then they go stiff and a cable change does not seem to help. I am not a lover of "Gripshifters" and that was after I inherited a Good quality bike with good shifters fitted. I just don't suit them.

Cable tension is almost surely the problem and, as other posters have indicated, it's generally very easily fixed.

BUT. Yours have already been readjusted once. As a general rule, once is enough. Try this: Examine every place where you have a cable housing stop. What you are looking for is 1 or 2 little tiny wires sticking out of the cable stop. If you find that, your cable housing is gradually shortning itself. That will require either repeated readjustment of the cable tension, or reterminating the cable housing. If it was my bike I'd do the second.

I am game for changing the shifters. I would like to go to thumb shifters. Is this something that I can do myself? I am game fr giving it a try. If I hose it up I can always run it over to the LBS.

Had grip shifters for years - no problems. Wife still has them and they are fine. I now have a bike with trigger shifters - they work ok too.

Change shifter if you want, but you'll still need to be able to make cable tension adjustments with any type of shifter. If that is a challenge, I would not think about doing the shifter replacement on your own.
The part you need right now is at about 3 minutes.https://bicycletutor.com/adjust-rear-derailleur/

Rotating grip shifters are just fine. Like any other shifter stye they do need to be properly adjusted. That can take som tweaking. In that respect they are no different from the Shimano 105/Ultegra setup on one of my bikes. Just keep working with the LBS techs. They should be given an opportunity to get it right and they probably will.

I am not a fan of Gripshifters either, I love friction.

The biggest advantage to grip shifters (good high dollar one's made by SRAM) is that they move almost twice as much cable per gearshift as most other shifters. In theory, this makes cable stretch half the problem it is for others, same with dirt and moisture. The adjustments just last longer. Good for mountain bikes in the woods.

SRAM x.7 is ok, X.9 is quite good and X.0 is superb but simply unaffordable for most. Most other gripshifters are mass market and not such good ideas. If you have one of these latter, then almost any lever shifter will outlive it as the guts of mass market gripshifters are plastic and even inexpensive lever shifters are metal.

The high end SRAM also require a matching rear derailleur also by SRAM as it must also work with the doubled cable ratio.

It's an acquired taste..........not suitable to all..........very different.

It isn't at all unusual to have to rotate the shifter slightly past the desired gear and then come back to it, especially with low-end shifters.

Higher end SRAM MTB lever shifters pull as much cable per shift as the grip shifters. This is a trait of SRAM components, not just their grip shifters.

That's true..........their Grip Shift technology has moved over to their lever shifters. I've tried them and I guess it's a case of old dog and new tricks. I just can't get enthusiastic about having to move my thumb over and shift when all I normally have to do is move my wrist a bit like moving the throttle on a motorcycle.......think click done.

I imagine that's what most of you feel like with levers as well.............