Compose three same-level pieces into the next level (one Lv5 = 81 Lv1 pieces). Cheap sourcing, in priority order: (1) patrol incessantly - the single most important source; (2) buy monarch gear whenever it shows on the Black Market; (3) spin the Wheel of Fortune daily. Patrol method: refresh with gold until a gear appears, then buy it for 30 gems; do ~30-100 refreshes/day. About 100 refreshes yields 30-40 pieces for ~1,000 gems (vs 24,000+ gems at the store). Black Market Lv3 gear appears at ~200-600 gems/item - but do NOT buy Intellect Crown or Strength Crown there (they cost the same 1,800 gems as the store). Wheel of Fortune gives random Lv2/Lv3 gear (10 spins = 900 chips; also a tavern activity quota). Timeline for free/low spenders: Lv5 gear in 1-2 months, Lv6 in 3-4 months.
Original research source: Evony Guide Wiki