You can book tickets for the Heathrow Express online.
http://www.heathrowexpress.com/index...7-0F7782CBBA06**
It's much quicker, about 15/20 minutes, than taking the tube all the way, which takes over an hour.
The hardest bit will be getting from Euston to Paddington. It's only about a mile and a half away, so if it was a quiet time of day you could take a cab. What I'd do is leave Euston station, walk to Euston Square underground station, which will take only five minutes, and then get an eastbound Circle Line train the three stops to Paddington, where you can then get the shuttle to the airport.
http://www.heathrowexpress.com/index...7-0F7782CBBA06**