Try this. It can't get much simpler.
sync on:sync rate 60
Rem Load Ten Single Images (Frames) For Sprite Animation
digits$="_00"
for frames=1 to 10
number$=str$(frames)
index$=left$(digits$,3-len(number$))+number$
load image "walk_down"+index$+".bmp",frames
next frames
Rem Get Screen Size
sx=screen width()
sy=screen height()
Rem Setup Sprite
set sprite 1,0,1
sprite 1,0,0,1
Rem Determine Sprite Screen Max. Limits
slx=sx-sprite width()
sly=sy-sprite width()
Rem Center Sprite On Screen
x=slx/2
y=sly/2
do
Rem Check downkey
if downkey()=1
y=y+4
frame=frame+1
if frame>10 then frame=1
endif
Rem Test Sprite Limits
if x<0 then x=0
if x>slx then x=slx
if y<0 then y=0
if y<sly then y=sly
Rem Draw Sprite To Screen
sprite 1,x,y,frame
Rem Update Screen
sync
loop