You and Dina go on a quest to find Abby and her group. The following spoiler free walkthrough for The Last of Us 2 covers the starting sequences of Seattle Day 1.
Reach the gate
You and Dina ride through the woods - pass abandoned vehicles and you will reach a small building. Go inside and search it - you will find, e.g. a map. It will come in handy in the upcoming chapters taking place in Seattle.
Get back on your horse and continue the way forward. After a while, you will reach the large gate - you aren't able to go through it. Climb up the crates to reach the top of the truck and walk towards the ladder.
Grab it with Dina's help and jump onto the nearby scaffolding. Walk it to the end, then jump onto the platform next to it. Jump lower and slide to the other side. Jump one more time and go to the other side of the gate.
Opening the gate
Go down the ladder and walk to the power box. Try to activate it - the power has been cut. Break the window in the trailer and go inside. You will find a locker with codes for various gates - it will come in handy many times later.
Now go to the generator in the back of the trailer and start it. Pick up the cable and open the gate. Come with the cable to the power box and attach the cable. The nearby gate will open - you can search the area. Unplug the cable you put in before and go back a little bit to where you found it - throw the cable over the fence to the other side. That way, you will be able to pull the cable to the next fuse box.
Now go inside and approach the panel. You can enter the code to the main gate - 0512. This code is written on the paper with codes you found earlier.
Dina will join you. Get on your horse and ride forward. Soon, you will reach East Gate 2. Go to the generator and try to start it - you will find that there is no fuel. Time to do some searching.