Arduino sending data over MAX485
How would the wiring look like? I was unable to find any dumb-proof
  tutorial online.


I found this tutorial to be pretty usefull.

There really isn't much to it, I suggest trying a short range before going full range.
It's a "half duplex bus system" the ends of the bus should have a "end termination resistor", usually 120Ohms, between the A and B signal.
Since it's half duplex, the Pi and Arduino can't talk at the same time.
You'll have to pull the DE and RE pins high when you want to transmit (and keep them low for receiving).

Basic sketch would be something like:

#define TXEnablePin 13

void setup(){
  Serial.setup(9600);
  pinMode(TXEnablePin,OUTPUT);
}

void loop(){
  String data = "";
  Unsigned int sensorValue1 = Sensor.getValue();
  Unsigned int sensorValue2 = Sensor.getValue();
  data += str(sensorValue1) + ":" + str(sensorValue2) + ";\r\n";
  send(data);
  delay(10000);
}

void send(String data){
  digitalWrite(TXEnablePin,HIGH);
  delay(1);
  Serial.send(data);
  Serial.flush();//Wait for everything to be transmitted, before disabling transmitter.
  digitalWrite(TXEnablePin,LOW);
}



  I don't know whether or how to use the logic level shifter.


These things are pretty straight forward. You should actually be able to figure it out yourself (given you have the power of the internet).

LV to 3.3V of Pi
GND to GND of Pi
GND to GND of Arduino
HV to 5V of Arduino

Then, whatever 5V signal you want to connect to HVx and whatever 3.3V signal you want to connect to LVx

Example:
Arduino-TX -&gt; HV1
Arduino-RX -&gt; HV2
Pi-TX -&gt; LV2
Pi-RX -&gt; LV1





  If I can read the data over serial port, would it be just a plain text
  (as shown on PC in Arduino ide serial monitor), or has each value its
  address that I could then easily accessing to a variable then being
  used to process the weather data?


It would be ASCII (plain text) if you send strings.
You could make different types of requests.

Like; If you send: "Temperature" to the Arduino, it will respond with: "TEMP:10" or something.

But the easiest thing would be to send all values of all sensors in a combined string every 10 seconds or so. And let the Raspberry Pi unpack that string.


  If I'm completely wrong in something, or there's some completely
  different way how these things are being done by more experienced
  people, I'd love to hear some suggestions.


I think it's pretty good that you actually already know of the existence of RS485 and why you'd want to use it.

But I also feel that you feel a little uncomfortable with the project as it is.
It's important to handle problems one by one, to avoid getting overrun by problems.
Try to make it working over (short) USB first. Then try a short RS485 link and eventually try a long RS485 link. You can then more easily spot where the problem is. Use facts from multiple tutorials, to boost the confidence you have in the system ;). It may just work if you wire it as said. If it doesn't work, you can always post a question.

If possible, it may also be worthwhile to follow some tutorials on Arduino (get a starter kit and book with tutorial projects?). Within these tutorials they give examples of problems and show what there is to solve them. Without throwing yourself into a dark pit of a project.