You can mine with the wallet client. Go to the debug window, console, type in "generate "  ie.  "generate 10"
It will then keep trying to generate hashes until it reaches the number of hashes you dictate for it. But that doesn't mean that every hash will be a winner on the network. So you might get only a fraction of coins for the hashes you output (competition with network processing power). Also, note that the client can get stuck when generating hashes manually like that, and if you try to exit before it finishes the # of hashes you told it to crunch, then it will hang and need to be force closed (or wait until it finishes all the hashes). If you wait for it to finish, you will notice in the console window it outputs a list of all the hashes it generated and at that point you can exit the client without problem.

This has nothing to do with staking coins. It is standard crypto mining wherein the mining is performing the action of blockchain Tx processing and validation. So your mining is helping the transactions on the network.