Usage patterns
〈場所〉に蜘蛛が巣を張るfor a spider to spin a web (somewhere)
A spider had spun its web under the eaves.
蜘蛛に刺されるto be bitten/stung by a spider
I got bitten by a spider while working in the garden.
蜘蛛が這うfor a spider to crawl
I noticed a spider crawling on the wall.
Expressions
平蜘蛛のようprostrating oneself; lying flat like a flat spider