Note: While completing missions make sure that you do not have your bandana equipped if you own one. Wearing one while completing story missions or side missions will cause you to not be rewarded your fame or honor points from the mission.
Fame and Honor will come from progressing through the story missions. Every time you complete an objective you will be rewarded with Fame or Honor points. Raising and lowering your Honor level is a lot easier and will require less effort. Decide what path you want to take and stick to it.
This will unlock at some point later in the game. Complete as many activities as possible. Once you get close to the 100% completion this should unlock with any issues. Just make sure you don't stray your either good or bad honor, as it will just waste time. Raising your Fame bar will take longer than your honor bar so make sure you help people at the side of the road and complete all the misc tasks.