BurnBob
Best option is to dig holes(should be easy due to rain) then use stuff called Postcrete which is specifically for posts. Very simple to use. Dig hole, post in, fill hole with water then pour bag of stuff in. Will be solid with 5-10 minutes. Fiver a bag or so. Put at least a quarter of post in the ground, fence posts, rails and slats are all standard sizes, use screws rather than nails.
This works but you also need to think about the post rotting after a few years. – Form the postcrete into a dome/slope up to each post so that water will run away from the base of the post.
Might also be painting or preserving the base of the post at the same time.
Oh and if you have any trees or large shrubs in the area, you WILL find a root in the wrong place. ‘Mutts’ are good for cutting through such things and post hole diggers can make life easier as well. More info