The I-90 Trail, known as the Mountain to Sound Greenway, or the John Wayne Trail, depending on how far east you are on the trail.
Section 1 - Seattle to West Lake Sammamish - 15 miles
The trail begins at Dr. Jose Rizal Park. From there the trail winds east to the bike tunnel parallel to I-90. The bike lane on the Dearborn is the easiest way to get under I-5.
Cross Rainier and take Haiwatha to the start of the trail. Almost immediately you will come to a junction, take the left path. There will be signs as well; in fact there is excellent signage on the trail through Bellevue.
The map below shows the trail up to the west side of the I-90 bike tunnel
View Bike: Dearborn To I-90 Tunnel (west end) in a larger map
Upon existing the other side of the tunnel, there's a nice viewpoint and good rest spot.
The trail crosses the lake on the north side of I-90; the trail is wide and safe. Once across the lake, the trail winds east and ends at 118th, just under the I-90/405 interchange. The Lake Washington Trail heads south along the lake.
View Bike: I-90 Trail (east end of tunnel to 118th) in a larger map
Make a right and follow the signage. You'll go 50-100 ft, then cross the street and U-turn to find the trail continuation:
The I-90 trail continues east from Factoria via a bike lane along 36th. This portion represents one of the 'gaps' in the trail system and so you must ride the bike lane along 36th, a fairly busy road.
Follow the lane until you reach 150th SE and then the follow the signs to cross over I-90. Here's a wide view of the area:
And a close-up of the crossing over Eastgate. As of 2012, this was the busiest part and has the most interaction with traffic. There is a project underway to improve that section, but I do not know the estimated completion date.