Hi. I feel a bit ashamed to ask this, but on my first attempt to change it I lost. I don't want to break it, so I tried to figure out how to do it easily.
Check the images:

It seems easy, isn't it? There is that small button thing to press and move up, right? Usually there are two, one for each side, and then I can move the lamp or open the sides. Well here I can't.

On the other side there is a wall (fridge).

Is this a mounting error from the landlord or am I missing the right wrist movement to open it?

(I should have posted this as anonymous, I know )

Not 100% sure but i think you need to turn it and then you can easily take it out? You can see it with a new one: it has 2 pins at the end on both sides.

Difficult to be sure, but it looks similar to one I have (not where I'm typing from tonight). And I think the whole end piece should be able to move to one side if you activate the button thing, allowing removal from the fixed other side.

open the clips, turn the lamp...

If I press the clip on the left side (first picture), I can move that side a bit to the left, but it doesn't come out.

What do you mean with "open" the clips?

The end caps should slide off

Then rotate the bulb 90 degrees and it should just slot out.

No luck.
The left side moves slightly to the left, but it doesn't either come down or go more to the left. The lamp doesn't move at all and the right side is useless.

What's the red thing for? check if you can do something with it and take the left cover completely out.
If the tube is a cylindrical one, you should be able to rotate it towards you slightly, and it will come off.

The red thing is a switch. I think you can pull the white end pieces downwards, then the clear plastic cover comes off, then you can pull the tube downwards, it has two plugs.

I had a lamp like that in my first flat, took me ages to figure how to open the damn thing when the neon tube died out . Some el cheapo design from the 60s, really annoying. The left side should either slide or pull down, Sbrinz has got it right.

I was able to pull the white part at the end. I had to pull it to the side.
I wasn't able to do that because this lamp shouldn't stay against a wall. There are two "switch" for each side, so if I can only reach one switch, I can't really "unlock" it. Anyway some day I tried again and somehow it unlocked.

The problem now is another.
I've bought a new lamp, tried it but it doesn't work. I thought the problem was the starter, but this thing doesn't have a starter, or at least not like I thought.
It should be like this one: http://www.osram.com/_global/pdf/Con...x_combi_el.pdf

I suppose I have to give up and call the Hauswart