What does it mean?

Freezing:

Freezing is the act of stalling the lane. The position of both team's minion waves is considered to be the position of "the lane", or rather, the active zone. By freezing you're making sure that the lane doesn't go into the enemy turret nor to your own turret, effectively 'freezing' the lane.

Fast Push:

When you want to do a fast push, you essentially attack minions with everything you can in order to make your minions go foward as fast as possible.

Slow Push:

This is a bit more tricky, as it combines elements of both. Ideally it means you're freezing the lane, but without letting your minions die in order to build a massive wave.

When are they used?

Freezing:

You freeze to deny farm and you freeze to be safe. If you're able to trade damage better than the enemy, when you correctly freeze your lane you can easily attack the enemy when he goes in to farm. This is especially useful on botlane (As none out of 2 characters will be taking farm). It's also used to protect yourself, as if you're ganked (if you've frozen the lane near your turret) you can easily go back and either stay safe or force the enemy to towerdive you. The same is valid for the enemy, if you managed to freeze near your turret, he's going to be too far away from his own turret and as such if you begin winning a fight (whether due to a gank or not) the enemy will have a much harder time to get away from you.

Fast Push:

Quite simply, you want to push. If you want to towerdive, you should at least try to get minions under the turret in order to take less damage. Other times you may have someone trying to help you with a gank, but they can only come from behind the enemy turret, and by pushing a lot you can get your minions under the enemy turret (which will not only tank at least 1 or 2 turret shots, but you will give vision which is extremely important on towerdives. The same is valid if one of your teammates has a high range ability but can't see that 100 hp enemy laner (eg: Lux, Xerath, Ziggs). There's also two other reasons which involve pushing in order to not have enemy minions close to your turret (especially useful if the enemy has the baron buff, making them take longer to get their minions to your turret), or if the enemy can't farm under turret (for either not waving good wave clear or not even being in lane). Oh, and obviously, when you want to put as much damage on the turret as fast as possible. However a slowpush may be more effective.

Slow Push:

It's not that easy to pull this off. You want to push as slowly as possible in order to get as many waves of minions with you, effectively freezing the lane. However you also need to keep the minion wave alive and that means that you'll have to make the enemy minions shift aggro often in order to not kill your own minions. Once you're satisfied with the ammount of minions you have on your side, you can begin a fast push, and have 2-3 waves of minions attacking the enemy turret, which forces the enemy not only to miss some farm, but makes his turret take massive damage.

How to

Freeze:

• Make sure you only last hit, and at the last moment
• If you can, group the initial minions of the enemy lane (by standing in front of it and taking a few hits before it reaches your lane)
• Don't let enemy minions reach your tower, take the hits instead (if you can) while your own arrive

Fast push:

• Give all you have to kill everything

Slow push:

• Kill the caster minions of the enemy lane to let your own kill the melee ones
• Leave the lane, it will then do it alone, but make sure you build pressure somewhere else so an enemy champion doesn't come to clean your building wave of minions
• Ideally start this far from the next enemy tower to make sure the wave has time to stack

What for

Freezing:

• Helps you farm close to your tower (safe)
• Forces enemy to come close to your tower to farm (unsafe)
• CAREFUL : While you are doing this, opposing champion may be creating a play on another lane. Freezing a lane is useful but takes a lot of time, make sure it handicaps the enemy, else it is handicapping your team.

Fast push:

• The opposing champion backed, make him loose xp by crushing your lane on the tower before he comes back
• Make your minions come to the enemy tower for a tower dive
• Reset the lane to then start a freeze on the next one

Slow push:

• Prepare a slow push before putting pressure elsewhere, the enemy team will then have the choice to stay grouped and deal with you (and your team), or to send someone deal with the big minion wave you built before it destroys a tower.
• CAREFUL: For a slow push to work, your whole team needs to put pressure on the map to make sure enemy doesn't send a champ to clear the wave while it is building.