There are not many ways to get to Solden, just drive yourself or take the bus.
During winter period there are many busses going there, so that is an easy and quick way to get there.
Other way is to fly to Innsbruck and take eaither bus to Solden or the train to Otztal Bahnhof and from there it is with the bus again. As you guessed, by train you can get as far as Otztal B., but then it is on with the bus.
Of course Sölden has got modern chairlifts and cable cars too, realy most of them are prety new. There are some 2 and 4 Person chairlifts and some chairlifts wich cary 6 persons. Some of the chairlifts have got "bubbles" wich can be put down in case of bad weather to protect you, lucky us we didn't need to put the bubbles down :)
This is one of the oldest Chairlifts in Sölden, the Chairlift to Hochsölden. Its apparantly about 60years old.
Its only one person per chair and there is no footrest so you leave your feet hanging in the air, a funny feeling. Not very usual for skiing places is that you don't leave your skis on your feet but hold them when you are on the lift, wich makes geting on and off the lift lots of fun....
There are Skibusses in Sölden to get you to the Cablecars and back to your accomodation after Skiing.
You can use the Bus free as guest in Sölden.
The Busses run from about 8.30 in the morning until about 18.00. The Timetable ist displayed at every Stop.