Increase your reputation by contracting contracts.
The easiest way to improve your reputation in MechWarrior 5 is to contract the various contracts littered with the Starmap. First of all, we need to divide your reputation into two categories: clan and faction.
Clan reputation is your biggest concern, as it unlocks additional campaign quests and grants you more negotiation points at all levels. Faction reputation only applies to the faction you are helping or fighting: take contracts for a faction to raise it, and take contracts against a faction to reduce it.
A clan's reputation is easy to level: all you have to do is enter into contracts. All contracts offer reputation, but if you see a high reputation quest (yellow icon) on the Starmap, complete it for a large reputation reward (and sometimes a mech or a handful of powerful new weapons). These usually have multiple pieces, so be sure to save a little to keep up with repairs.
The reputation of factions is a bit more granular. You can check the information on any system you select to see which factions are under control and which factions you are likely to face. The colored sectors of the Starmap also indicate which faction controls that sector (and therefore, will likely sponsor your efforts in the region. Maximizing a faction early gives you more points for negotiation, so it's safe to focus on one faction. early and stick with them for a while if you want to maximize your grind. High reputation quests and multi-objective quests are great for leveling up your faction rank, but remember this: you can't mend between objectives in a multi-objective quest, so grab them when you have a stable of mechs and pilots to swap between.
Be careful: failing or canceling a mission can cause you to lose reputation, so try to save before accepting a contract or quest to avoid this penalty.
That's all to increase your reputation: take contracts to increase the rank of your clan and use the information on the Starmap to focus on the faction you are in to maximize the rewards. For more guides, be sure to keep an eye out for our guides page.