Ensure that the weather you want is actually possible. Snow in summer is a big no-no. It's not going to happen. Be careful what weather you pick. I can't stress this enough: don't try to make it storm if you aren't an experienced atmokinetic. Try to make a light breeze the next day at 10:00, or make the sun come out at 12:00.
I prefer to lie down for this step, but you could stand or sit if you want. What you need to do is imagine energy flowing into your body, filling you up but not escaping.
When you feel ready, imagine yourself as a beacon of energy. All of the energy you have built up is flowing into the sky, but you are still gathering more energy and sending that up as well.
The energy that is in the sky should be imagined as a web of thin threads of energy, cupping the sky (if you wanted a cloudy or cloud-less weather phenomenom, if you want things like a breeze you have to imagine a cube of threads running through the air).
This is the really tricky bit. This is the most difficult part if you can manipulate energy. You need to imagine three things at once. Keep imagining energy going into your body and up into the sky, forming a web or cube, then at the same time you need to imagine the weather you want taking place, and also a time. Try to imagine yourself seeing an alarm clock, and you should set a reasonable time; rainclouds aren't going to gather in 10 minutes. Do this for as long as you mind can stand it.
Wait. If it didn't work, don't be disappointed. It may not be your day, or your ability. By all means try again, but it's a very difficult process that requires so much imagination and concentration that it's almost impractical.