How to design an RF reader?

Do you mean by Bipolar transistors on PCB? For RF Front-end, you can definitely do it. I know some products are purely based on NPN and PNP, not IC.

Yes on the pcb, we are starting a project on RFID and we thought it would be wise to design our own reader so can anyone has the circuit or the link to teach so.

Yes of course you can.... depending on how much you want to "do". You can get a basestation IC and go from there, or use a module, or something like the U2270B etc. Plenty of options. Just Google away...