I have completed the services requested, now the client is refusing to pay the balance owed (3000 owed on 7000 total). I want to try and collect this legally. The client is a lawyer. What are my rights? Can I go to their home? How often can I call? Can I mention the non payment to others also providing design services to the client?

It does not matter that the client is an attorney. What matters is whether your contract will show when you expect payment for work done - and whether you did the work or not.

Do you have a contract with him?
Did you complete the work?
Do you have these records in writing?

If so to all of the above, you can take him to small claims court regarding the amount due.

As for your other questions:

Yes, you can knock on his door or call him for payment... but do NOT do so frequently or at odd hours so that he will not have a good counter claim against you for harassment.

Bottom line: Sue him if you have backup documents to support your claim.

Presuming that you finished the job and he is not paying after giving him the final bill: What is he saying to you as to his not paying?

What RickJ said.

Also, consider filing a mechanic's lien if, according to the law in your jurisdiction, one may be filed. This may "encourage" payment, particularly if the customer is planning on selling the premises any time soon.