What steps should I take to obtain a CA signed certificate that verifies a public key used to do create digital signatures? One constraint is whatever coding that's needed will need to be done in Java.
Depending on what kind of signatures is needed, you should be looking for different certificates, eg. code signing or office doc signing or other types they offer. By following the links you will learn all details about the procedure.
In brief - on your client computer (usually via browser) you generate a keypair that consists of the private key and a public key. Then the public key is embedded into Certificate Signing Request (CSR), which is sent to the CA (again usually via browser). And the CA sends you a signed certificate, which you then merge with your private key.