There are many ways to program it. One of the popular device is USBtinyISP and DASA. Both of them work very well with WinAVR (AVRdude).
I'd like to share how I program ATtiny85 with JeonLab mini 1.3. The idea has been adapted from High-Low Tech Group and provideyourown.com. One missing note from High-Low Tech Group is that you need to add a 110-120 ohm resistor between VCC and Reset pins of JeonLab mini (or Arduino) to prevent Auto reset on serial connection as explained in here and here.
Step 1: Schematic diagram
Step 2: Assembly on a prototype board
9 (red, right): Heartbeat - shows the programmer is running
8 (red, middle): Error - Lights up if something goes wrong
7 (green, left): Programming - In communication with the slave
You can also use a bread board as shown in the 3rd picture.