These things will raise a Pokemon's friendship:
Ribbon Syndicate massage
EV berry
leveling up
vitamin
Veilstone City massage
battling a gym leader, elite 4 member, or champion
128 steps
learning a TM or HM move (make sure you don't break copyright law when using a trademark move)
X items (including dire hits and guard specs)
These things will lower a Pokemon's friendship:
fainting
surviving poison outside of battle (probably doesn't apply to Budew)
bitter herbs
source
The easiest ways to evolve Budew are probably leveling up, EV berries (any of the 6 except Hondew and Tamato), vitamins (specifically the calcium and carbos), and the Veilstone City massage. Use a soothe bell if you can.