It sounds like you need to swap TX and RX, and maybe you're missing the ground connection as well.
Tx means transmit, and Rx receive. So Tx of the FTDI cable needs to connect to Rx of the arduino, and vice versa.
Using this diagram:
Connect DTR (Arduino) to DTR (FTDI), TX (Arduino) to RX (FTDI), RX (Arduino) to TX (FTDI), Vcc (Arduino) to Vcc (FTDI), Gnd (Arduino) to Gnd (FTDI).
If that doesn't work, disconnect the DTR wire, and manually press the reset button just as the Arduino IDE finishes compiling.