Dresden is one of Europe's most beautiful cities, with exceptional art, music and architecture, but with no direct flights from the UK, the best way to see the city is to fly to Berlin and combine your visit with a stay in the German capital.
Berlin has so much to see, (especially the museums) that I would recommend a minimum 3 nights there. The city is also quite spread out so using the U-bahn or S-bahn is the best way to get around, as well as being very reasonably priced.
The Hauptbahnhof (main station) in Berlin is an amazing modern glass structure on 4 floors with shopping and many restaurants. If travelling 1st class you also get access to the 1st class lounge with complimentary drinks. From here, Dresden is approximately 2 hrs by direct train.
Extensive renovation has turned Dresden into a fascinating, safe and beautiful destination for opera fans and lovers of the Baroque. It is easy to walk around and I was amazed at how some of the buildings we see today had only recently been resurrected from their ruined state.'
I would suggest no less than a 2 night stay, then you can visit central Dresden, with its churches and museums (the Frauenkirche and Green Vaults are unmissable), and also take a trip by paddle steamer along the River Elbe to see the surrounding countryside, with its pretty castles and impressive villas. Why not stop off for lunch at one of the many riverside restaurants, all serving local food, or take a ride up the cable car to the panoramic cafe - restaurant Louisenhof, to enjoy tea and cakes?
Having visited in summer, I would definitely return to both cities in winter as well, when it would be lovely to see the Christmas Markets.