Cochin is a breeze for most as handily it has an international airport. It's about an hours taxi journey away from where the magic of the Run happens in Fort Cochin (traffic permitting). If you can't find a flight directly in or out of Cochin that suits you, then you can easily get a flight to a bigger transport hub such as Mumbai. An airport taxi will cost around £10, or there's a rather marvellous AC bus you can take for about £1.
It is now possible to fly to Jaisalmer. Other options are via overnight train to Delhi, which is extremely reasonable depending on what class of ticket you get. There is a ridiculously detailed website about Indian rail travel here. Trains should be booked in advance as they do tend to fill up. You could also fly to Jodhpur, which is around 5-6 hours away by road. A taxi will probably cost you around £40, or you can get a train or bus also for much less.