depending on what you run AWS EC2 instance is the easiest method to do it. You can get free trials for very small machines.

I have the same issue but just run it from home as

1) added cost to run a decent server (m3large is $ 189.59 per month)
2) significant cost to move my database into the cloud. ($902 per month)

If you run the cheap low machines its ok but they probably won't be quick enough for what we need.

Overall while there is great benefits in the cloud its very costly and not worth it. I can run a redundant server at home for backups for just one months cost in the cloud.