How to install deck railing post sleeves on these posts?
Making some dangerous assumptions here...
You'll be removing everything between the posts so that you can slip the sleeve over the top, then reattach everything, right?
While you've got it all apart, take 2 of your post covers and cut one complete side off so that you've got a U shape and slip it on by pressing toward the house. You will likely have to cut each remaining side individually to fit exactly against the house to have a nice, flush finished look.
On the post in the 2nd picture, you can probably slip the sleeve between the wood and the vinyl siding so it won't have to be a perfect cut, just long enough to cover the gap.
On the post in the 1st picture, you'll want to scrape the paint off so you've got a nice surface on that (currently) white trim, then scribe the post cover to fit nice and snug up against it.
Once you've got each of the modified post covers fitting the way you want, run a bead of construction adhesive (like Liquid Nails™ - check the label to ensure it's compatible with wood and your cover material) on each inside edge of your cover, then slip it on and probably apply a couple of clamps until the adhesive is set.
Finish by reinstalling all the railing between the newly covered posts.