Option 1 - Googe Maps shows the fastest route to be going from Missoula to Lolo, and head west on State highway 12 west to Kooskia, ID, turn southwest on State Highway 13 to Grangeville, ID, turn south on State Highway 95, which will take to Interstate Highway 80, which will take you all the way to San Francisco going through Reno, NV and Sacramento, CA.
Option 2 - Another way is to go go west on Interstate 90, Go south on State Highway 395 which will take you through Pasco/Kennewick/Richland area and to Interstate 84, go west on 84 to State Highway 97 and go south which will take you through a bunch of small towns and Klamath Falls, then turn south on Interstate 5, which will take you I-80 and then to San Francisco.
Option 3 - take highway 93 all the way down to interstate 80 which you can take to Portland to Interstate 5 or highway 97.
Option 4 - variation on option 3, take highway 93 from Missoula, Just past Challis, take highway 75 which will take you through Sun Valley, ID and to Interstate 84 and highway 93. Can either take 84 to Boise, ID and continue to highway 95 which you can take to interstate 80. Or you can take 93 to interstate 80.
Option 5 - Take i-90 through spokane to Seattle, and then i-5 to I-80 and to San francisco.