Thanks for writing. You've reached the easy part now...do nothing! Wait until autumn after the foliage turns yellow, then cut it all back to the ground. In spring, the asparagus will send up new spears, a few of which you can harvest but you'll want to let most grow out and feed the root system.
Keep your asparagus watered during times of drought and feed it in spring with a general-purpose garden fertilizer or compost if you wish. Otherwise, there's not much to it. Your plants will grow and get bigger and better every year.
---Justin, Senior Garden Editor, BHG.com