Metal Gear Solid 2

Gripgauge

You can hang down from the railing of the tanker right at the beginning of the game already and watch your gripgauge get smaller and smaller. The first time someone, this time the Colonel, mentions it ingame is as soon as you step on the AB-Connecting Bridge with Raiden. Then the Colonel explains what I explain here too, but I do this better and more elaborate, that's the reason why you are reading here and not listening to the Colonel. He seems to play with you all the time anyways.

Hanging

As soon as you are standing next to a hiphigh obstacle, mostly a railing (you recognise railings from by being able to partially see through them, meaning they have struts in them and you can see your player character behind it) you can swing over it by pressing your action button and then hang from this thing.

If the room under the object is less than one length of your player character you will not hang from the railing but just stand on the ground one level below as Raiden or Snake don't think it's any use holding onto the railing any longer. You can see what I mean when jumping over the smaller pedestals on the outside of the Tanker or the railing inside of Strut B. But there are more than enough other railings to jump over.

Once you are finally actually hanging from a railing, be it above an endless abyss or above some platform you can jump down to, you will notice that a new display appears, this is your gripgauge. This gripgauge empties over time and once it reaches the last fifth (1/5), is starts beeping and shows you this way that your character is running out of strength.
As soon as the gripgauge reaches 0, when it is empty, Snake or Raiden losen their grip and drop down. When you are hanging to the outside railing of the Tanker or on a connecting bridge of the Big Shell then you fall down to your death. If there is (metal gear) soild ground below you, you land on this and lose some health depending on how far your dropped.

When you just want to drop or jump down without waiting for your hero to run out of breath press the

button. Use this to your advantage as you can get behind soldiers this way and get to them in a way that you normally wouldn't be able to do. You can also jump on their heads and knock them out this way. So this is another way to get rid of them.
If you want to pull up again in no time without dropping down just press the

button again, your character pulls up without problems.

Pull Ups

Grip Level 1
So you avoided being spotted and are hanging from a railing and don't know what to do now, well, there is something you can do and it is even useful.
When pressing

at the same time Snake and Raiden do a Pullup. With the normal Gripgauge you can do 5-7 Pullups until they run out of power.
A pullup counts when you pulled all the way up without releasing the buttons before.

Grip Level 2
After doing 100 Pullups you get a call on your Codec and get the message that your Griplevel reached the next level.
So you trained your muscles and got stronger. With Griplevel 2 you can hold on longer without dropping down.

Grip Level 3
After another 100 pullups, that make all in all 200 pullups, your griplevel increases again to level 3. There is no level 4 for the griplevel.

Cheating on Pullups

So some of you get bored by doing 100 pullups or you just don't want to do it all that long, but you still want a higher griplevel, well, there is something for you:

It is possible to do 10 pullups at once, but... this is quite dangerous. When there are 2 railings on top of each other you can drop down from the top railing by pressing

and when you are fast enough, before passing by the lower railing, press

and you will grab onto the lower railing and can get onto the platform behind the railing from there.
You can use this tactically to get advantages while playing and on top of that this move counts for 10 normal Pullups.
You just have to take care to press the

on time and not accidentaly press

again instead of

as you will otherwise fall to your death most of the time.

So now you might be wondering where you can do this move and voila, here are some spots where you can do this, this list is no way complete, more like a pointer, there are even more spots where you can do this:

Tanker Level:
In the Engine Room are some places in the east where you can drop down from storey to storey, and remember, watch out to not fall to your death.

Big Shell Level:
Here the Strut D is a good place to train your muscles in no time. Inside the Sediment Pool it is very fast when doing this close to the stairs. Watch out to not fall to your death and not drop down at a part of the railing where the railing below is solid and has no possibility for you to grab on.