The Cap River is a crazy fishery. It makes my head want to explode everytime I go. The close proximity to the city brings out a very interesting range of people and you will see LOTS of instances of wilful disregard for any rules/regulations. Littering is prolific. Using bait during the bait-ban time is commonplace. Those poor fish get every lure in the book thrown at them. Anyway, that doesn't quite answer your question...
You'll find that access to the river can be challenging in spots. The river runs in a steep rocky canyon from above the Hwy 1 bridge to the fish hatchery. The rocks can be slippery and fisherman slip and fall in to the river every year.
Fishing is dependant on the river flow and the ocean tides. The fish seem to move in pulses. At this time of year there can be an early run of small coho that arrive. Typically they are caught in pools at first light (at this time of year that's like 4:30am).
As
@jim morrow mentioned you can access a spot under the Hwy 1 bridge by parking near the Chevron and finding the trail/stairs down to the river. I think that when the river level is up this spot kinda goes away but I don't tend to go there.
Most people congregate up at the Cable Pool which is just below the fish hatchery. There is a pedestrian bridge over the river there. Note that fishing is not allowed above the bridge.
My advice is this:
1. use small flashy lures
2. go for a walk and find spots to fish
3. beware of the slippery rocks
4. don't go if seeing the worst kind of fisherman behaviour will bother you (This is the reason I rarely go now).
Good luck!