DigitalOcean was mentioned above and might be worth trying if you're new to the mining game and don't have the money to invest in Bitcoins for cex.io, or for mining hardware such as ASICs, multiple GPUs etc.
DigitalOcean plans are cheap and you can get free $10 vouchers when buying $5 plans (search Google for latest codes). There are two downsides though:
1) If you don't already know Linux, you will need to get familiar with it VERY quickly to get it to work. There are some good tutorials about Dogecoins (but will help with other currency set-ups too) at
http://dogecoin.ga/.
2) The hash rates can be incredibly low so you will need to spend credit quickly to see any worthwhile mining results. I set up dual core server for Dogecoins (for fun) and could only get 6 Khash average. Even with the most expensive plan, you would be lucky to get over 35k.
You might be better off trying to invest in some altcoins for now unless you're willing to spend big bucks on hardware or cex.io, (who I'm deeply suspicious of).