From I-70:Exit I-70 just West of Green River on Utah Route 24. Head south on UT-24 for approximately 30 minutes. Turn right at the sign for Goblin Valley onto a paved(!) BLM road. Continue down this road until you come to an intersection and a BLM information booth. Turn left down the (newly paved) road to Goblin Valley.
From Bryce Canyon and points beyond:Take Utah Scenic Byway 12 north and east through Grand Staircase-Escalante National Monument until it meets UT-24. Follow UT-24 towards Green River (again, east and north), through Capitol Reef National Park. In the middle of nowhere, turn left onto the paved road to Goblin Valley. (Watch it - there's a 4WD back road into Goblin Valley before the paved turnoff - you don't want to take it.) Turn left onto another paved road at the intersection with the BLM info station.
Fees: ~$5 per car. 4-day passes are available, and are good for all Utah state parks.
Lodging: The park has no lodging. Green River and Hanksville are the closest towns with lodging.
Camping: There is one campground in the park (often full during the tourist season). There are BLM campsites outside the park boundaries.
Food: There are no food concessions in the park; the park has one picnic area, overlooking the valley.
Information: The park ranger and some informational signs are just about all there is for information. There may be some informational programs run during the tourist season.
Park Facilities: The park gates open at 7am and close at dusk. Campers therefore have more private access to the park during the early morning and evening hours. The main attraction in the park is the Goblin Valley itself; the entire basin is open for hiking. Two small trails lead to overlooks (and provide access to the valley itself from the campground).
Trails: As stated above, there are two small trails in the park. One leads from the valley to the campground via some badlands area and an overlook point. The other wanders off to the North of the valley. I have not yet had the opportunity to take either trail.
Little Wild Horse Canyon: This slot canyon is only about 3 miles outside the Goblin Valley park boundary. If you have never seen a slot canyon, have a couple of spare hours, and are not afraid of tight spaces (and if the weather is very clear), I highly recommend it.
Arches and Canyonlands National Parks: Moab and its sights are only 1.5 hours from Goblin Valley. In fact, chances are you came from there to here.
Capitol Reef National Park: Capitol Reef is the least visited National Park in Utah. Mostly this is because, on the surface, it doesn't have much to offer. A scenic drive only seems to follow a long cliff face through the desert. And its only other seeming attraction is the old Mormon community of Fruita. The key word is 'seems'. Capitol Reef hides many secrets, if you're willing to venture off the beaten track.
Grand Staircase-Escalante National Monument: This huge tract of land protects many slot canyons, desert rock formations, and historic land routes. Very wild, very undeveloped.