For the best results, don't actually look toward the radiant (the direction in which the meteors appear to originate). That's like looking up at rain. Instead, turn about 60 degrees (NNE or SSE) and look halfway between horizon and zenith (straight overhead).
The meteors may look close; they're really burning up many miles high in the atmosphere. Watch for bright meteors ("fireballs"). They actually can leave a glowing "train" of charged particles that persists for several seconds to minutes. Rarely, a sonic boom is heard.