The Last Guardian - Walkthrough for the first 10ish minutes
There are a lot of things to be said about The Last Guardian, but if you've just loaded up the game and are sitting in a cave with a wounded Trico and no idea what to do, what's to be said is what you need to do and a reminder of the type of game you're getting into.
Trico is not only wounded, but hungry and chained up. With no exit in sight, you have to alleviate the beast's pain and get it walking before you can continue. This is just the first of numerous situations with vague progression you're going to find yourself in.
Your future-self narrator mentions Tricos are man-eaters, and it seems plenty willing to eat you up if you get close. Luckily the chains and its weak state are keeping it from moving around too much -- you can't approach it from the front, but you can from the back.
There are a spear sticking out from its body, and removing it is as easy as holding the circle button and holding down to pull them out. Once you've removed them you have to find it some food to regain its strength. And what does it eat? Barrels full of glowing blue butterflies.
On the opposite side of the room you're in is a structure with three barrels. Two are easily visible and you can jump onto the platforms they're on to get them. The third is behind a door at its base, which can be opened by pulling the lever next to it. These barrels will serve to motivate, distract, and aid the beast as you progress. But for now it needs to eat and get strong.
To feed Trico, you simply throw or drop the barrels near its mouth one at a time. Throwing is probably easiest in this case since it gnashes at you if you get close. It's still wounded and is not ready to trust you just yet, but it will be soon. Feed it and get its strength back up. It won't eat when you're too close, so give it some space.
Once fed, you must climb its body and pull another spear from its shoulder.
It's time to deal with the last problem: the chains. Once Trico is up and moving around, hop onto its back and climb to the mechanism holding the chains. Pull the lever and it will free the beast from its restraints.
Now it can follow you out of that little area of the cave down to the little offshoot, in which you'll see some sort of vapor or cold air coming out of a hole on a ledge higher than you can reach. Luckily there's a barrel on that ledge, and Trico is always hungry. It gets distracted and tries to get the barrel, which gives you the opportunity to climb up its back, get the barrel in the fight hole, and then crawl through the hole.
You'll have to figure it out from here, as what you find is a spoiler. But one hint I can give is that your journey is for both you and your giant companion, and progress is often made with it rather than without.
Progressing in The Last Guardian is more obtuse than Shadow of The Colossus and this very small segment of the game is preparing you to keep your eyes open and make good use of the friendly Trico. Look for tiny holes and doors you can enter on your own as well as areas only the Trico can enter (and don't forget you can climb its back).
This is just the beginning of an adventure between a boy and his newfound massive animal friend. There are a lot of surprises in The Last Guardian, both in story and gameplay. With a keen eye and gaming sense, you'll be able to finish Team ICO's long-awaited adventure title.