Most gear you can test out in your house. Take your boots out on any trail, each time you go out pack a little bit more in your pack and get used to the weight. Come up with a good clothing layer system.
Make sure you can get your tent set up quickly. There is nothing like setting up in a downpour minutes before sundown. You can practice this inside.
Make sure you understand how to properly setup and use your water filter.
- Keep the input hose separate from the hose that goes into your bottle.
- Make sure you know how to "prime" it if necessary. You may need to take it apart on the trail, fill it with water and put it back together before pumping water.
- Make sure you know how to service the filter as well, it will likely get grains of sand in it which may plug it and prevent it from working. Or you may fall and crack it, what is your backup plan? Do you have something to boil water in? Do you have chemical water treatment?
Learn all your gear. Understand how the stove works. Do some tests with the fuel source outside in trail conditions and see how much fuel you'll need with your stove for that period of time.
Figure out how you'll sharpen your blades if it becomes necessary.
Build your skills, they come in as handy as gear does.
I'm sure you left it off on purpose, but I didn't see a mention of maps or compass. Learn to use a compass and read a map(and maps scales). Get a waterproof map of the area you will be going. Trails turn to crap quickly and all of a sudden you'll find sketchy 'flagging tape' to get you around closed off areas. Know the markings for the section you will be on. Markings usually have a meaning. Call ahead or check online for trail conditions.
Make sure you are prepared for the climate. It may be beautiful at the bottom of the mountain, but you may get smacked with a snow storm at the peak.
On a separate note, a construction size garbage bag is a great inexpensive liner to keep the inside of your pack and keep its contents dry. Bring an extra bag, they are cheap and light.
Bring some petroleum jelly soaked cotton balls in a pill jar to help you start fires. Lighters are awesome, but a backup source is handy.