if I buy the 315 MHz Wireless Data Modem Transmitter and Receiver Kit for Arduino
how do I program it so that when I turn it on it acts as a permanent booster/signal extender
so essentially works just like wifi booster
when turned on finds RF signal and sends it to transceiver which sends out signal to nearby RF unit
Did you mean "sends it to transmitter"?
The key problem here, is where the transmissions originate. Because, you have to decode a packet before you can retransmit it. Do you know the protocol? That would be the case if the source is another Arduino sending packets in a format dictated by your software. However, if it's from a consumer device, you don't know the protocol, and then can't decode packets.
So, you need to tell us more about what you need this for.