From the far East (Solon) far West (North Olmsted), or South (Strongsville, Brecksville): I would take I-480 to the Broadway exit, head north for about one mile. After going over an overpass, you'll see the park on your left. At the entrance to the park there's a big wooden sign that says "Garfield Metroparks" or something similar. Turn left at the light, veer right (the other way goes to the ranger station), go up the hill, and the fields are on your right.
From Downtown and near west side: take I-77 south, exit at Brecksville Rd, get onto rte 17 east (Granger Rd.) take a left on Warner rd, go up the hill, take a right on Garfield Blvd, follow Garfield Blvd until you reach Turney Rd, go straight through the intersection onto Garfield Park Blvd and it will lead you into the park, the fields will be on your left before you go down the hill.
From Heights Areas or University Circle: Take your pick of east/west arteries, and head west towards downtown. You can take Chester, Euclid, or Carnegie from the Circle or Cleveland Heights, or Larchmere/Woodland, Shaker/Buckeye, or Chagrin/Kinsman from Shaker and much of Cleveland Heights. All of these roads intersect with E. 79th. Turn left (south) and keep going. South of Kinsman the road goes under a RR bridge and swerves right. It has just turned into E. 78th, but you don't care. Just keep going. This road ends at Broadway. When you spill out onto Broadway, turn left. Follow the clearly marked overhead signs to stay on Broadway, and in a mile you will be at the park entrance on your right. Go up the hill, and there we are. (You may also wish to experiment with Woodhill/E. 93rd, but I find 79th moves better. More importantly, I feel safer on 79th.)