The following is a very brief summary walkthrough of Journey.
The easiest way to play the game is to merely 'walk towards the mountain'; the mountain is the only goal, and aside from the glyphs and symbols there really isn't much else to do (unless you wish to run around aimlessly and explore). This walkthrough is a possible route one could take in Journey, although it's much more beneficial to go along on your own.
Aside from the walkthrough, you may want to collect the PS3 Trophies, Ancient Glyphs, or Glowing Symbols.
The Beginning[]
Walk up the sand dune to begin the game. Walk toward the first pile of rubble to pick up your first glowing symbol. Head toward the mountain and you will enter "The Hub" where you can pick up two more symbols. Climb/jump/fly up to the top of the middle tower and fly across to the glowing area.
The Bridge[]
There are three glowing symbols you can pick up in this area if you want. Otherwise, Hold 
Circle by the long pieces of cloth to transform them into pieces of the bridge. When it is rebuilt, run across it to the next area.
The Desert[]
In the desert, you will discover Cloth Creatures that you can occasionally fly. Follow them through the level, or head out on your own toward the mountain. You will get to a sandstorm area where you must climb a tower with the help of some cloth creatures. At the top, hold Circle to release more creatures and continue on to the next section.
Note: You can find the Hidden Desert Flower in this area for a trophy.
The Descent[]
You will surf down through a destroyed city. If you glide through 15 columns you will receive the Adventure trophy. You will have one resting period where you will have to push Circle by long pieces of cloth to unlock a cloth fragment cyclone that will carry you to the next surfing part.
The Tunnels[]
In the tunnels you will have to evade Guardians with spotlights -- if you are in the spotlight when it turns red, the Guardian will tear your scarf. You will also encounter new types of cloth -- long seaweed like cloth that allows you to seemingly swim through the air and jellyfish-like cloths that boost you up to their tops.
Continue through the tunnels, evading the monsters. At the end, the monsters will chase after you until you surf through a magical barrier, which concludes the level.
The Temple[]
In the temple, you will have to find different glyphs and hold Circle to illuminate them. For each glyph magical "water" will rise. You can swim through the air and power up quickly. There are four different glyphs you must find to make the water rise to the top. Climb the tower in the middle to continue.
It is possible to get through the temple without raising the water at all, but you must have gained most, if not all the symbols up until this point. Zigzag upwards to higher and higher platforms/roofs. There is no achievement for this, but if you make it to the side room without raising the water from 2nd level to 3rd level, you can see the whale swimming in a circle on the ceiling and even go up there and play on its back.
The Mountain[]
There are no glowing scarf pieces in The Mountain. The Mountain is the most difficult level and is very emotionally draining. The snow will drain your scarf's energy. You will have to battle through strong winds, so hide behind some stones during the slow winds. You will also have to evade some more flying spotlight monsters by veering far to the side or hiding under blocks. You will get weaker and weaker but must walk along a cliff up through an entryway. Avoid more wind gusts as you walk through a broken building. The final section is a windy, snowy section. You will continue to get weaker and weaker until you finally sink into the snow.
The Summit[]
A being will wake you up and send you flying to the summit of the mountain. You will have a full scarf and seemingly unlimited energy. Fly to the top of the mountain where you will reach your final destination.