Web Swinging
Your quickest way through the city will involve swinging on your web line, which you can do by pressing "R2." Pressing "R2" each time you start to swing back down will keep you swinging in that direction in a seamless motion. Press "R1" to use your webbing to zip to a surface directly across from you, which is useful for quick attacks against enemies in your line of sight. You have a finite amount of webbing, but it does regenerate slowly and automatically.
Web Attacks
Several special web attacks can be used against ordinary thugs and supervillains alike. Press "Down" and "Triangle" to use your webbing to yank an enemy toward you for easier close-range attack. "Left" and "Triangle" will give you temporary boxing gloves made of webbing to make quick work of enemies. "Right" and "Triangle" encases you in a protective "Web Dome," which is useful when being confronted with multiple enemies. "Up" and "Triangle" fires your "Impact Webbing," which is handy against foes at long distances. You also can press the "L1" button to manually aim your webbing at a foe.
Effective Attacks
Press "A" to jump and press "Circle" to kick while still in the air to clear an area around you by knocking down multiple enemies. You can't do this twice in a row without needing to cool down briefly, so use this attack sparingly. Press "Triangle" plus either "Square" or "Circle" to grab an enemy and perform either a combination punch (with "Square") or kick (with "Circle") attack. Kick combos have a greater reach than punching combos, so those are your best bet if you're surrounded by enemies.
Spider Symbols
Different coloring on the spider symbols indicates a different effect. Blue symbols give you additional webbing cartridges, up to a maximum of 10. Red-and-white symbols give you additional health. Gold symbols give you temporary armor and a temporary attack boost. Gold-and-red symbols give you Magnesium webbing, which is useful against symbiotic enemies like Venom and Carnage.