A good way to get rid of spider crickets or any other crickets is to use some sticky glue traps that will trap the crickets without any harmful chemicals.
To keep spider crickets and other crickets out of your house get rid of any damp areas by drying the damp areas out around your house.
The crickets like damp areas so ridding the damp areas will keep the crickets out of your house.
You can also make a cricket trap using molasses and some water. The crickets will be attracted to the molasses and jump right into the bowl and eventually drown.
Be sure to take your trash out often as well to keep the crickets away.