The first thing you should do when you arrive at a park is stop by the visitors center. No matter how much research you do in advance, national parks still operate in a somewhat analog manner, often posting the most accurate weather concerns, trail and road conditions, events, and other announcements on-site. Talk to park rangers, and ask for advice on their hikes or must-see stops; they may have insider knowledge about how to beat the crowds. Learn at the park’s museum about the history of the land and animals to look out for — and, of course, be sure to get your passport stamped.
It’s important to start slow and small when hiking, even if you’re a seasoned veteran, to understand the park’s layout. Most parks have an short and easy “discovery” trail leading from or close to the visitors center. These low-impact trails are intended for less mobile visitors to see a snapshot of the park but shouldn’t be overlooked by more ambitious hikers. Some are geared toward educational exhibits, like the Fossil Exhibit Trail in Badlands. Others serve as examples of the landscape, like the Discovery Trail in Joshua Tree. Spend time acclimating to the park on easier trails before jumping into anything bigger, as you may find factors you overlooked and need to adjust your schedule.
Unless you have extensive experience hiking alone in the wilderness, do not hike anywhere other than an established, maintained trail. None of the parks I’ve visited required an off-trail excursion to embrace the beauty of feeling totally immersed in nature. There are plenty of groomed trails that are sparsely hiked. Stay on the trail, and hike smart.