Ice Cave is pretty self-explanatory, except for a few sliding puzzles. 
Before you enter, you have to remember a couple things.  First:  pick 
up all of the items you see!  At some point you will find HM 08, and 
you will need it to get to the Pokémon League.  You will also find some
 useful items, such as Point Up (PP Up), which I used on Lugia's 
AeroBlast attack.  Second:  bring someone with Strength.  For the 
first sliding puzzle (probably the hardest), start out on the normal 
ground right below the ice.  From there, go up, left, up, right, up, 
right, down, left, up, left, down, right, down, right, up, and right.  
That should take your target, more normal ground.  From there, keep 
walking until you find a room with four holes in the ground.  Save your
 game, then start moving the rocks you find around.  You need to get 
all four of them to drop through a hole, or you will find it impossible
 to continue through the cave.  After you have pushed each one into a 
hole, go down any one of the ladders in the room, or just fall down one 
of the holes.  You will land in a square room with normal ground and a 
ladder in each corner, normal ground with a ladder in the middle, and 
ice surrounding all of them.  If you got all of the rocks to fall down 
the holes, getting through this room is very easy.  Make your way to 
the normal ground in the upper-right section of the room.  Stand on the 
outermost (lower-left) corner of the normal ground, and move left.  
One of the rocks you dropped in the holes should be there to block you.  
If it isn't, then you started from the wrong place.  If it is there, 
move down to the next rock, then left, up, and right.  You will land 
on the normal ground in the middle.  Go down the ladder into the next 
room.  From the ladder in the next room,
go right until you find another ladder.  Go up it.  From where you 
are now, go up and right, then onto the ice.  Get up to the stairs, 
get on the platform/hill, and go down the stairs on the left side.  
You should land on some ground in the middle of the ice with a ladder
on it.  Go up the ladder.  Directly after all this, there is another 
sliding puzzle.  Starting at the stairs, go down, right, up, left, 
down, left, down, and left.  Go a little deeper into that normal-ground
arena and you will find an item that you need.  Get it, then go back 
to the ice.  Starting from that normal area, go right, up, right, up, 
left, up, left, down, and left.  This will put you on more normal-
ground.  From here on, it's just an easy walk out of there=)