How to properly put 2013 Prius in storage for the next 6 months ?

My concern is with the warmer temperatures, the winter tyres get softer and thus the sidewalls may not be able to hold up the car while it's parked for an extended period of time. If it's possible for you to get it done on your own with little to no expense, I'd switch out the winter tyres and put on the summer tyres.

In any case, I would pump the tyre pressure up to close to the sidewall maximum because your car won't be driven. Of course remember to deflate them back to normal pressures before you start driving (maybe leave a note on the dashboard or somewhere where you'll see it before you drive off).

If the car is in the garage, the solar panel battery maintainer won't work, will it? Alternatively, you just take the 12V battery out (but you'll lose radio station presets and may have to re-initialize the auto up/down windows and moonroof (if equipped). @Mendel Leisk will have some helpful tips about 23V battery maintenance.

A car cover (if parked outside) helps but make sure it's tight over the car so that animals can't get in and nest or shelter.

6 months should be ok (as long as it's in the garage will reduced temperature swings as opposed to being outside on the driveway).

As for the hybrid battery, before you park it, make sure it's neither full (7 or 8 bars out of 8) nor empty (2 or 3 bars). It usually likes to sit somewhere in the 3/4 mark according to the Energy Monitor (about 6 bars out of 8 bars). That's about 60% real SOC.