Monarch EXP raises Monarch level, which caps how far Generals can be leveled. Best F2P method: Shrine Offering - up to 10,000,000 EXP/week possible at Shrine Lv35 with 6+ gem-paid offers/day (cost escalates 25/50/100/100/200/200 gems, resetting daily) plus free 'Tribute' offerings and Monarch Talent 'Offering' for +20% (max at monarch Lv5). Tributes come mainly from Relics (best - collect 25 fragments, break the tile with a hammer for a chance at 10), then Alliance Shop (10,000 points each), then Black Market (300 gems/5 or 500 gems/10), also Wheel of Fortune/Lv2 Candy - roughly 100-180 tributes/week obtainable this way. Other ranked sources: Crazy Eggs event 230,000+ EXP/day (~12-day event); killing Hydra always gives EXP - chest gives 5,000-17,000 (Lv1-5) plus a flat 3,500 EXP per kill regardless of chest; normal monsters Lv31+ give 2,600 EXP each (Lv30 and below not worth farming); Resource Tiles Lv13-15 give 10,000 EXP each, Lv16 gives 20,000; Dwarf's Lucky Apple gives 22,500 EXP if lucky. Battlefield Shop/Black Market EXP purchases are explicitly not recommended (bad value).
Original research source: Evony Guide Wiki