Commerce centre's are a facility, I think there's an NPC one in the starting city of each home planet but I could be mistaken. Trading stations you have to be able to get into space for and get to one that allows the public to use it (as there all privately owned). Centerpoint is a unique station that is privately owned, I believe they may buy for you but not allow you onboard.
All allow you access to the NPC market, where you can buy a very limited selection of entities, mainly a few ships and vehicles. The further away from the entity you are the more expensive it is. As a new player you will be able to afford nothing so don't worry about this for now.
Also in commerce centres (I think, might be an other shop like facility but i'm pretty sure it's commerce centres) theres an NPC you can talk to to buy very basic items you don't need but can probably afford.
Otherwise you have to buy directly from players by looking at the trading boards, joining the trading channels on IRC, the player run market web sites (centerpoint's faction page leads to one of them) or by contacting the factions that produce what you want. On the rules page the words "affiliated to" mean those factions have the datacards to produce those entities. By visiting the faction's web site you should be able to see if there selling, at what price and contact details. Theres also a list in the traders lounge of the rpg centre.
However you will be able to afford bugger all upon starting, join a faction and they will pick you up, teach you the basics, answer any questions and provide you with all you need as time goes by. Initially that will probably be a ship as items aren't fully implemented yet. You won't own it, but you can use it. The faction will also pay you so you can save up and buy you're own stuff.