The easiest route to follow -by far.

By far the easiest way is to take a flight from Don Muang airport.

It only takes a little over two hours,there are a number of airlines taking this route but I prefer 

Air Asia,I find it easier to check in on the computer before leaving home,this can save you time 

standing in queues especially if you're traveling light with only hand luggage,you can go straight to
                                                      Immigration

Malaysian clearance is very quick and  troubles free for UK passport holders anyway.

there is a fast rail city link there now,but I had time to spare so took the bus instead, they run

fairly frequently.and arrive at the same place as the train be it on a different level.

I was staying overnight at a Hotel close to the Thailand Embassy so had to take a train to the twin

towers area ,when you leave the bus you have to climb  to the next level to catch the train the

ticket dispensers require you to add your destination plus the correct change there is a small 

kiosk there issuing small change,you have to travel about 5/6 stations.on arrival, you really want to

make your way to the front of the twin towers from there you can negotiate the road Jalan
Ampang past the Thailand Embassy, it's about a twenty-minute walk,there are buses and taxis
                                    that pass there but I preferred to walk

.

Don't be afraid to ask anyone for help nearly everyone speaks and understands English and

they are very helpful.They don't always tell you what you expect to hear,The Hotel where I

 had booked in was just passed the entrance to the Embassy but a little distance off the main

road,I had wandered down a road in the wrong direction so asked this man who was in his

garden before I had a chance to ask the way he warned me that I was in a dangerous area there

had been a number of attacks on people in that area recently.when he finally put me on the right
direction for the hotel which was not far away,needless to say, I didn't go out after dark.

The following day I went to collect my visa which was trouble free,I had left a lot of documents to
                 support my application so didn't expect any problems really.
I then started to make my way back to Bangkok which was a reversal of the same journey 
going.very easy and enjoyable If you're worried about catching your flight I would suggest you take
                                             the fast trains link back to the airport