The problem - a white, burnt out sky is caused by an exposure to long for the skys brightness. This problem is exacerbated by the lack of dynamic range in digital camera sensors. Whilst our eyes can cope with a range of light representitive of 25 EV(Exposure values, or stops), digital cameras are typically in the region of 4EV. Personally I'd sooner they improved dynamic range than making a gazzillionpixel sensor!
Solutions - Where possible, try and utilise manual exposures in troublesome conditions. The scenarios most likely to give burnt out skys are overcast days, backlit shots and if the sun goes behind a cloud in the foreground area only. It is also preferred, where possible to shoot in your cameras RAW mode. If you don't have RAW, always use the largest JPEG file size available as memory cards really are ten a penny (the 8gb tiny one for my phone cost me £9 with sd slot adapter). When you are photographing in these conditions, it's also advisable where time permits to take a practice exposure. This is the best way to see what you're getting. But do bear in mind the likelyhood of change in the conditions if shooting manually. If your camera has an option to display the test shots histogram, you should check this as it is more accurate to show you any blown highlights than judging the LCD image. For anyone unsure on understanding histograms, here's a useful link
this way please.
A final piece of exposure advice, more for the RAW shooters (and if you have a dSLR, there's no excuse for not using it). When considering how to expose your shots, remember that it's easier and less degredating to the final image to recover the highlights from the sky. Up to about +1EV, via studious usage of RAW software it is possible to recover highlights - if the sky is too burnt out when you try to recover it, it will become blue. If you take an exposure that has the sky properly esposed and the train underexposed, the recovery of shadows will mean you get a lot of grain and noise (random colour errors due to a lack of light received by the sensor), so where possible always expose for the shadows to be correct.
Graduated neutral density filter were mentioned, and I'm not going at length to explain these (if you want to know more,
click this link), but the main thing for them is you reduce the skys brightness but not the lower 'ground level' stuff. The main thing against them is the decrease in light reaching the sensor. This generally means slower shutter speeds and higher ISOs, both not desirable to pictures of trains in motion. This is why traditionally ND grads are used for landscape photography, particularly sunsets. That said due to better high ISO performance, they are more viable, along with their use on fast prime lenses and preserved railways with their lower running speeds.
I hope this answet has served to help people rather than confuse, if I'm going to answer a question, I'll always do so to the fullest and best of my knowledge. And cheers for the 'expert' tag Ferret, I just need the 'expert' kit like you now!