This is one of the more meaningful things someone can do, and the fact that you want to is worth honoring. Whatever his circumstances, a child reaching out is something most incarcerated people receive with more openness than you might expect.
The first step is locating him. If you know his name and the state he is in, the state department of corrections offender search tool will tell you which facility he is at. For a life without parole sentence he will be in a state prison rather than a county jail. InmateAid's inmate locator is another resource if you are not sure which state system to search.
Once you have the facility confirmed, send a letter. That is the right first move before any visit or phone call. A letter gives him time to process what he is reading, to sit with it, and to respond thoughtfully rather than being caught off guard by a call or a face at the visitation window. Keep the first letter simple and honest. Tell him who you are, that you were adopted, that you recently learned about him, and that you wanted to reach out. You do not need to have a perfect script. Just be genuine.
InmaneAid can send that letter for you with their return address on the envelope, which keeps your personal information private until you are ready to share it. That is worth considering for a first contact with someone you have never met.
If he responds and the communication feels right, the next step is applying for visitation approval at his facility. That involves submitting a visitor application, a background check, and his confirmation that he wants to add you to his approved list. The process takes a few weeks but it is straightforward.
Take it one step at a time. Start with the letter.