It's definitely possible to use Azure for free without the risk of incurring charges.

The free services are easy to identify in the Portal, and you should be able to apply a spending limit on your account. I'm sure last time I checked it was possible to set this at zero and you could also sign up without entering any payment details.

I am not sure about Azure, but you don't get charged on AWS for sure if you use the "Free-tier" resources.

They'll tell you which of the instances is eligible for free-tier when you are creating them. You get about 750 hours of compute each month for a year, which means you can run your free server for free for a year. They also give a free RDS (relational database) instance to get you started.

You'll be charged about $1 of activation charges to check if your card works and is compatible with their payment system so that you get charged in case you use more than the free-tier limits.

If all this is daunting, you can check out Google Cloud Platform, they are giving out $300 for new users. But you'll have to give card information to get started.

If you just want to get started with cloud, without all the hassle of managing separate instances for compute, database, storage etc, try Digital Ocean. They are not running any promotions but their pricing is pretty straight forward. The basic plan starts at $5/month which gives you a pretty good exposure to cloud computing.