Here are some common verbs from each group.
Group 1
aruku (歩く) --- to walk
asobu (遊ぶ) --- to play
au (会う) --- to meet
hairu (入る) --- to enter
hajimaru (始まる) --- to begin
iku (行く) --- to go
kaeru (帰る) --- to return
kakaru (かかる) --- to take
kaku (書く) --- to write
kau (買う) --- to buy
kiku (聞く) --- to listen
matsu (待つ) --- to wait
motsu (持つ) --- to have
narau (習う) --- to learn
nomu (飲む) --- to drink
okuru (送る) --- to send
omou (思う) --- to think
oyogu (泳ぐ) --- to swim
shiru (知る) --- to know
suwaru (座る) --- to sit
tatsu (立つ) --- to stand
tomaru (止まる) --- to stop
tsuku (着く) --- to arrive
uru (売る) --- to sell
utau (歌う) --- to sing
wakarui (分かる) --- to understand
warau (笑う) --- to laugh
yomu (読む) --- to read
Group 2
kangaeru (考える) --- to think
miru (見る) --- to see; to look
neru (寝る) --- to sleep
oshieru (教える) --- to teach
taberu (食べる) --- to eat
Group 3
kuru (来る) --- to come
suru (する) --- to do