Pinnacle peak is the signature peak of the Tatoosh range, a small range just to the South of Mount Rainier, and almost entirely in the park. It is composed of old lava flows, so the rock goes from almost solid to pretty awful, choose your routes accordingly. The easiest route is 4th class, and it is a fine option for those wanting something more exciting than a dayhike. The summit views North into the heart of Mt. Rainier, and south to the the Cowlitz watershed and Mt. Adams are sublime.
Follow 410 to paradise, or, if coming from the East, drive in via Stevens pass. Park at the Reflection Lakes parking lot, and follow signs for the trail. The trail lazily switchbacks for a time in dense forest, before beginning up to the Pinnacle-Plummer saddle in earnest. From the saddle, the trail deteriorates, and 3rd class scrambling ensues. The rock is almost solid from the hundreds of ascents, but beware of loose rock anyway. No special equipment needed for the standard route in summer. In winter an ice axe is mandatory, and conditions might require crampons as well.
There is a fee to enter the park, the best thing to do if you plan on visiting several National Parks is to buy a Golden Eagle Pass, which are good for one year and cost $65.00.
Overnight backpacking permits are required, quota's are followed. No need really to overnight, unless you're planning a multi-summit traverse of the Tatoosh Range. No climbing fees or permits are required for the Tatoosh, unlike Rainier.
Spring: An exciting snow climb, or wet depending on conditions that year.
Summer: Dry rock but crowded.
Fall: Less crowded, the winter storms usually hit late in October, and don't quit until....
Winter: Stable conditions required to decrease avalanche danger. This area receives huge amounts of snow.
There are crowded car camping areas in the Longmire area, and backpacking sites fill quickly as well. You can apply for a backcountry permit which enables you to camp anywhere that's a quarter mile from a road or trail, check with rangers for special zones that are an exception to this.
Mt. Ranier web site //www.nps.gov/mora/