Pierre is roughly in the center of South Dakota. This is part of why it was chosen as the state capital - to sit between the larger cities of Sioux Falls and Rapid City. I-90 intersects the state east-west. Pierre is not directly on I-90. One must take I-90 to Vivian, SD then drive 34 miles north on US 83 to reach Pierre.
From Sioux Falls, Travel west on I-90 to exit 212 (Vivian, SD) then travel north on US Hwy 83 for 34 miles. Approximate travel time is four hours.
From Rapid City, Travel east on I-90 to exit 112 (near Wall, SD). Travel east on US Hwy 14 for approximately 57 miles until it merges with SD Hwy 63 in Midland, SD and the road turns north. Continue for another 21 miles. At the intersection with SD Hwy 34 turn east and continue for about 30 miles to the city of Pierre. Approximate travel time is three hours.
River Cities Public Transit is demand-based and you have to call in advance to schedule a ride. Information is available here. 
Be sure to check out the capitol building, an imposing and impressive structure in a beautiful setting. You'll get a great view of it from across the river in Ft. Pierre. Take a tour and see the interior as well, from the hand-laid mosaic tiles on the floor to the intricate paintings on the dome. The sculptures outside are also worth a look. The Fighting Stallions out front might not be your style, but the energy they represent is clear. The memorial statues of soldiers out near Capitol Lake are also impressive.