Transportation from St Pancras to Isle of Wight

There are three main ferry routes to the Isle of Wight: Portsmouth-Ryde, Lymington-Yarmouth and Southampton-Cowes. Depending on where you want to go on the Island, that may be your biggest decider

For all 3, you need to get to London Waterloo station to take the train. That isn't actually too bad though. From St Pancras, follow the signs to the underground (there are lifts and escalators available). Take the Victoria Line (light blue on maps) to Oxford Circus, and try to be towards the front of the train. Follow the signs to the adjacent platform for Bakerloo Line Southbound (brown on maps) to Waterloo. It's a step-free change, and can be done in under 30 seconds if you're towards the front of the train and level with the tunnel linking the two southbound platforms.

Then, take a train to where you want to take the ferry.

For the Southampton-Cowes route, there's a free shuttle bus from Southampton Station to the Red Funnel ferry terminal, and you can buy a through ticket from London to Cowes including the ferry. Red Funnel have page covering the public transport options.

For the Lymington-Yarmouth route, you take a fast train to Brockenhurst, do a step-free cross-platform change to the Lymington train, then the ferry goes from the pier terminal pretty much next to the station. There's info on the Wightlink page, click to expand their Public Transport section to see it all.

Otherwise, look at the Island Line promotions page for details of some of the offers and deals for the through train-ferry tickets. (Island Line is the name of the train operator on the island)

Following on from Grzenio's answer

From Portsmouth there are 3 ways to get to the Isle of Wight, the easiest is the WightLink FastCat, the terminal for this is at the end of the platform at Portsmouth Harbour station where most Portsmouth bound trains terminate. This goes to Ryde Pier and takes around 22 minutes.

There is also a WightLink car ferry that goes to Fishbourne, this is around a 10 minute walk from Portsmouth Harbour station.

http://www.wightlink.co.uk/

Its a little harder to get to but there is also a hover craft that goes from Southsea to Ryde, this is about a 30 minute walk from Portsmouth Harbour station or there are buses that go from the bus station outside Portsmouth Harbour station, I only mention it as the only passenger hovercraft in Europe so it a bit of a rarity.

http://www.hovertravel.co.uk/

If you go to Southampton the Red Funnel car ferry and fast cat both go from Town Pier, and there was last time I used it a free shuttle bus between the station and the pier, and both go to Cowes.

http://www.redfunnel.co.uk

Looks like the shuttle bus is free if you have a Red Funnel ticket (or through train ticket), and £1 per journey per person if you don't, and runs every 30 minutes on a Sunday.

http://www.redfunnel.co.uk/travel-connections/bus-connections/citylink

If you're strictly seeking to minimise the number of changes at the expense of flexibility, and the ferry options from Portsmouth detailed elsewhere sound most suitable, then you can do it without using the tube at all - St Pancras to East Croydon (or Gatwick Airport), and then from there on to Portsmouth. This will be somewhat slower than going via Waterloo - a touch under 3 hours, with trains only every hour.

Only caveat is that the St Pancras to East Croydon route is often closed for engineering works at weekends - but you can check for your dates using the National Rail website. Search from St Pancras to Portsmouth, and put in the "More options, railcards & passengers" section that you want to travel via "Elephant and Castle". If nothing with a single change comes up, then the rail line through London is probably closed that day.

It depends heavily on where on the Isle of Wight you are trying to get to. Public transport on the island is relatively slow so it may be better to spend a bit longer on the mainland to arrive in the right place on the island.

With all of the routes from London your first job is to get to Waterloo or Victoria. Unfortunately there is no direct tube line to Waterloo, so you will have to change somewhere in London on that route. For Victoria you could get the circle line all the way but I expect it would be quicker to change (the Circle line is a pretty slow way of getting aroud)

If your aim is to be on the island as quickly as possible your best option is probably Waterloo -> Portsmouth Harbour -> Ryde Pier Head on the Wightlink catamaran. Other options in a similar area are the Hovertravel hovercraft from Southsea hoverport and the Wightlink car ferry from Portsmouth to Fishbourne but they don't connect as nearly with the trains in Portsmouth. IIRC there is a bus from Portsmouth and Southsea station to Southsea hoverport, I'm not sure what the situation is with the Fishbourne ferry.

For Cowes you would instead get a train to Southampton and take the Red Funnel or Red Jet services. I'm not sure exactly what the connecting arrangements are there.

For Yarmouth you would get a train to Brockenhurst, then a train to Lymington Pier and then the ferry to Yarmouth. IIRC the ferry terminal in Lymington is pretty close to Lymington Pier station.

P.S. Technically it's possible to get from Ashford to Portsmouth harbour without going via London but the routes are pretty slow. The planner is giving me routes either via Hastings and Brighton or via Tonbridge and East Croydon.