How do I start garnishment proceeding without going through a lawyer?

Before you can garnish anything, you need to obtain a judgment first. Depending on the amount and the court, you may or may not need an attorney.

Once awarded a judgment you then have to apply to the court for a writ of garnishment. Depending on what you are garnishing and the rules of the local court, you may have to provide specific info. For example, if garnishing salary you may need to legal name of the employer, their legal address, maybe even their Tax ID #. To garnish a bank account you will need the name of the bank and may need the exact account number.

Once the writ is granted you hire a sheriff to serve it on the holder of the asset.

Agree with Scott, have you already gotten a judgement ?