As you play through No Man's Sky, you will occasionally come across locked doors or pieces of technology that requires an Atlas Pass to open or interact with. The Atlas Pass is a craftable key card divided into three different types: v1, v2, and v3. And as of now it is not known how to exactly obtain v2 and v3 of this key card so I will only discuss v1 here for now.
Keep in mind that I accepted guidance from Atlas at the beginning of the game, so I'm not sure how the process goes for those of you who decided to explore freely. In any case, you should receive a transmission alerting you to the presence of a special monolith after making 4 or so warp jumps. Track down this monolith and interact with it before returning to your starship. Once back in space, you will receive another anomaly transmission. Follow that one to an Atlas Station. Grab the warp cells in here before speaking with the entity. Make another warp jump after and you will be alerted about a space anomaly.
Make a stop on this special space station and speak with the aliens there. One of these aliens will provide you with the recipe for the Atlas Pass v1. You should be able to craft the key card at any time from here on out, so long as you have the materials to do so.