How to analyse a game?

Basically you should go through your game manually first and write down move after move what is happening and so on, to the best of your ability. You don't have to write your thoughts after every move of course. After you are done, you turn the engine on and see what does the engine say. Try to figure out why is the move good or bad. If you do understand - for instance you will surely understand if you just hung a rook why is that a bad move, write it down and try to figure out what you could do instead.

Here is a general guide that can help you improve and just so happens to have a few sentences on how to analyze your games.

Definitely the question of the week. If not of the year.

How to analyse!

How to analyse rated around 350 (OP) or around 1400 (me)?

Not easy to answer.

The principle is probably the same. Look at the game manually and write down what you see in that pgn file you've downloaded. Then turn on the engine and see at the things engine finds out. Write down only if you do understand. For instance the move you've played  is a blunder. Try to understand why manually, then check it with the engine. If it is a one move blunder and you've just hung your queen write it down as it is straightforward. If it is more subtle, go through the engine line, and if you do understand the idea - for instance you've managed to trap your rook which is showed after 2 opponent's moves, a 400 rating player might not see it, but you will. So you should write it down, he shouldn't probably. If it is some very subtle thing where the position is not clear, you just discard it. Sometimes you will not understand the best or the second best move offered by the engine, but the third best will be still winning as it is the most straightforward. Discard the first 2 if you don't understand those, write down the third best move.

1. It is completely true. What I mentioned is the ideal analysis. I cut corners as well , especially because I play an hour per side and I can notice many things during the game, so manual analysis is not redundant but by playing longer time controls, you cover most things you would in manual checking anyway. So I do it from time to time like this. 

2. Yeah, but by checking the engine lines you might learn something. Many times you will not, but that is ok, we are not GMs so it is natural to miss certain things. In some games some of those will be very subtle and not that important to find anyway, as the difference between +0.6 and +0.3 is not that pronounced anyway.

i like to first write down what i thought about my moves during the game and then turn the engine on, cause the engine often shows important lines/ ideas which i can use in my future games.

Going through the game and finding mistakes is a way to analyze a game, yes. You can also use a computer to look over a game, chess.com even offers an analysis option under learn -> analysis, both more in-depth a limited number of times per day and a casual analysis where they still give basic lines you can look through. You need to be able to recognize what is going on though, and it's probably best to start by reviewing your own game yourself before using a computer to find things you might have missed.'

I skimmed over your game and mentioned a few simple things to look at. A computer can tell you some nifty tactics, some you may not understand, which is fine, you don't have to use it all. But some you will follow. Use what you can understand, if it isn't something you can realistic foresee noticing in a random game, don't worry about it yet. There will be plenty of straightforward ideas you can use. A computer bases their analysis on the players being able to see what it sees, which the players in your game will not be able to, but they also catch obvious blunders of hanging pieces, assuming there isn't some insane tactic behind it nobody thought of, lol. 

I didn't mention everything in that game btw, there's still stuff to catch. That mate in 2 wasn't the only checkmate shot you had on them. There's all sorts of stuff to pull out of that game. 

Well, that and a lot more things on how to improve you may find here:

https://www.chess.com/blog/nklristic/the-beginners-tale-first-steps-to-chess-improvement

Basically after you finish the game, you download pgn file. Then download a tool with an engine, like the free one I've mentioned in that article. Then you load pgn in that tool and you will have your game loaded. Then go through moves without an engine first, write something down after the moves, what were you thinking about the position, what did you think was the plan for some opponent move etc. After you go through entire game, turn on the engine and see what it does.  At first you will understand very little, and that is completely fine. In a few months you will surely understand more.