Do you have the correct drivers installed? From memory the ESP01 requires a seperate USB-TTL converter. You can test by looping TX to RX on your USB-TTL board and making sure you get characters echo-ed back to you in your serial terminal.
My old connection notes from when I tried to use the ESP-01 ( I quickly moved on to boards with more IO pins and on-board USB)- perhaps you need to pull RST high as well as CHPD?
USB to FTDI adapter (make sure set to 3v3)
Adapter(l-r with ftdi at bottom) -> ESP-01
DTR
RX -> RXD0 (7)
TX-> TXD0 (2)
VCC
CTS
GND->GND (1) but wired jumper back to pwr supply
On ESP-01 need to have RST (4) and CH_PD (6) pulled high for normal operation.