Hello
I wish I had a resource like this when I first got here a few months back but thanks to patient reading and a few helpful players, I managed to find my way to the in game console and found how to check my own ping and fps rates. This is obviously a mere fraction of what you can do via the console and I welcome any feedback and discussion to this thread and will edit the original post accordingly should there be some absolutely essential console commands people feel that everyone should know.
With that said, let's get started, with pictures!
Groundwork: Go to your game library and right click dota, you should get a screen looking like this:

Here, you click properties to get to the next step, which is "Set Launch Options" and write down -console

This enables you to open and use the console. Close window, launch game.
In game, the first thing that'll hit you will be something like this:

Otherwise business as usual, but you'll now have the console open by default. You can close this by selecting the console and clicking the key bound to toggle it.
The key that is by default the console toggle is tilde (~), which apparently is located next to 1 in the corner of the keyboard for most keyboard layouts. For nordic keyboards this isn't the case and you guys will have to bind the console to another key, because the default key simply doesn't work.
There is a workaround for this, however, and it's doing this in the console as it opens when you start game:
bind "f11" "toggleconsole" with the default being bind "~" "toggleconsole". You can use any unbound key for the console.
As stated, you can only access the console while playing or observing and you obviously do this with your toggle key. When you do this, the game shifts to the main menu where you can now enter a command to the console. The command I created this tutorial for is
net_graph. When you open the console and write either
net_graph 1, net_graph 2 or net_graph 3, you will now be able to see your fps and ping in-game, like this:

To get rid of the net_graph, you enter the command
net_graph 0 in the console.
Obviously the console can do way more than this but I'm not experienced in using it. For me as a player ping and fps are interesting statistics and I hope this information will help at least someone.