Rewards in Imperialism are given for reaching certain "milestones".
We'll simply list the reward and underneath will give a brief description of "what it takes" to gain the reward.
Admiral[]
Build 5 Ships of the Line. Reward an Admiral plus a free Ship of the Line.
General[]
Build (or acquire Colony armies if playing peacefully though you'll still need to build a unit to actually trigger the reward) 6 armaments' worth of units (a regular counts as 1 armament, artillery 2 at the start of the game). Note that your starting units count towards getting this reward.
Subsequent Generals are ever harder to acquire as more armaments are needed. We'll update this later.
Army unit starts with 1 medal of experience[]
Conquer a Minor Nation's Capital (you'll also get a statue on top of your Armoury).
Expanded Capitol Building[]
Conquer a Great Power's Capital. Your recruiting rate drops from 4 to 3 provinces needed to recruit a new unskilled worker.
Expanded University[]
Build 10 Expert workers: reward 10 paper added to your warehouse stock.
Build a further 20 Expert workers (making 30 in all): reward a further 10 paper added to your warehouse stock.
Note that these workers must be in your labour workpool to trigger the reward.
Free Clippers[]
Reward for building first colony (even if you do not have Clipper Technology); you also get a statue.
Improved Railyard[]
Build a connected depot in or next to a village on the map. Also build a factory (not a mill) to capacity 4.
Allows industrialisation of villages.
An extra exploit if unable to reach a mining resource (for whatever reason - usually a lack of technology is involved) is to build the resource regardless and leave it unconnected, and you'll still get a steel (or higher) which is of higher value anyway.