How do I get from Pompeii to Positano? Is there a direct route?

Pompeii is difficult to get to from Positano by public transportation. But it can be done. This subject comes up here a lot, so I suggest you use the Search feature (top center), maybe with the words Positano and Pompeii. Only by searching will you believe the frequent recommendations to hire a car service! In April the public transportation will not be as badly crowded as in high season, but it will still take a long time, each way. Some people visit "on the way" from Naples, but I prefer to make day trips from my base city.

I don't there is anything direct from Pompeii. You could take the bus from Sorrento or the ferry. However, if steps are a problem, Positano is not the place you should be going. The whole town is mostly steps up or down. The bus would be better because it stops are either end of the town somewhat in the middle (top to bottom).

Good advice from Frank and Tim.
The variety of transportation from Sorrento around the region is a reason a lot of people choose to stay there. The main part of town is also relatively flat so there are a lot fewer steps to deal with. The ferries also sometimes can't dock in Positano on days that the sea is very choppy.

Pompeii is easy by Circumvesuviana train from Sorrento: only 30 minutes, and no train changes.

There's no direct transport from Positano to Pompeii. You can take a SITA bus to Sorrento or Meta and then the train to Pompei S. Villa Misteri:

Bus schedule (bottom of page)
http://www.sitasudtrasporti.it/archivio/Download/corse/sitasud/Campania/Salerno/07fdbd86-3667-4b12-8fed-a2ab69d516b7_QUADROXIV_INV_2015_2016.pdf/0

Train schedule:
To Pompeii:
http://www.eavsrl.it/web/sites/default/files/orariautomobilisti/Orario%20Sorrento_Napoli.pdf

From Pompeii:
http://www.eavsrl.it/web/sites/default/files/orariautomobilisti/NapoliSorrento_New2015.pdf

Thank you so much for your replies for how to get FROM Pompeii. We will be coming down from Rome & thought that we would visit Pompeii on our way TO our final destination which is Positano. We will be both bringing our suitcases so that's why there was a concern about the steps. We want to minimize the number of steps to carry our suitcases up/down to get to the Positano residence.

Question: 1) Is there a taxi stand at the train station of Sorrento? 2) Are there any good companies to look up for Drivers in Sorrento?

Nearly all train stations, except for very small, will have a taxi stand. Train passengers are good customers for taxis.

If you are taking the train into Sorrento and then the SITA bus to Positano, the bus stop is directly across from the train station. Taxis right there, too, but I don't know what they would charge for Sorrento to Positano.

Rick Steves, the sponsor of this website, mentions a few drivers in Sorrento in his applicable books. We usually stay at larger hotels, so we often start there for local referrals - we assume that they have a strong interest in satisfied customers, if you see what I mean.

In fact, the new Mercedes sedans and pleasant drivers we got through our Sorrento hotel were both excellent and a little cheaper than the estimates in Rick's book. While one is right to be suspicious about a relationship between a hotel and another provider, you also should consider the assurance it gives vendors that you will show up and that they will get paid. Our car service bills conveniently appeared on our hotel bill. So I think the general principle I'm suggesting is more valuable than the name of the local travel agency the Hotel Ambasciatori happens to use, Eurotravelsorrento dot Com Vigli degli Aranci, 9 80067, Sorrento

I'm confused why you haven't asked your Positano hotel how many steps there are to reach their door. Since Positano has only one road, there's little doubt about where you'll be starting on foot. Some hotels provide porters for this reason. I would doubt that the Sharing-Economy provides porters, if that's what you're using. I suggest that you also get quotes for a pickup at Pompeii Scavi, since the total travel time would be less than training to Sorrento first. Assuming there are porters, a driver could call for them to meet you pretty easily.

Since we will be trying to find our Airbnb rental which is a private apartment, the taxi from Sorrento seems better than the bus. And a Taxi would probably be less expensive than a driver. Is there definitely a taxi station at the Sorrento train station?

I was in Sorrento a year ago in May, there are a few taxis at the Sorrento train station (right near the buses), if you don't see one, wait a few minutes. Or there should be a phone number to call at the taxi stand.

Zoe is correct. But as I learned from my Rick Steves book, there are both legal metered taxis and legal unmetered taxis in Sorrento. They are allowed to use the same line at the Circumvesuviana station. Our unmetered taxi charged us 15 Euros, with bags, for a 3 minute drive to our hotel. When I saw how close the hotel was to the station, I felt this was a ripoff.

You need to understand that Sorrento to Positano is a very substantial drive, and a Sorrento cab has to consider the high probability that they will have to return empty. I would think that this is reflected in the cost of such a taxi ride. Taxis are not in business to lose money.