Lavender and lemon are both natural spider repellents, so using lavender and lemon around your house is going to deter spiders from hanging out for long.
You will need a good spray bottle. In the spray bottle add equal parts of water and vinegar. Example 1 cup water, 1 cup of vinegar. Add in a few drops of lemon essential oil, and a few drops of lavender essential oil. Spray this mixture everywhere spiders can access your house, around the doors, windows, baseboards. Spray around the foundation of your house, in the corners, up by the rafters, etc...
Now I have heard spiders come in through fireplace chimneys. Make sure you spray the lemon, lavender, vinegar recipe mixture around the outside of the chimney really good, and do it every couple weeks or so.
This is only a deterrent to spiders, but it has been known to help cut down the number of spiders inside a house by a lot. Does this kill spiders? I'm not sure if anything other than a predator kills spiders, but using the spider spray to cut down the number of spiders will help.
I've also heard spiders don't like chestnuts when they are in the ugly green stage with the thick green prickly skin. I'd be piling those up around the base of my chimney and around the base of the house every few feet, to help deter spiders. I don't have a chimney, but if I did, I'd use this method for sure.
Be sure to view my previous post about Keeping Spiders Out Of The House for more ideas that really work.