How to find the AppID of a game?

That's exactly the way I would do it as well: use a link of the of the respective steam store page.

In most cases you actually want to use the number in the javascript when you mouse over the buy button. Example: here the relevant ID for me is 13669. (because its actually the german low violence version for me shown there)
I also recommend the SteamDB script.

/app/291480/

Assuming you mean SubID: 47144

Edit: As for way steam://nav/console

Type:

] licenses_for_app 291480  
License Steam Sub 47144 (47144):  
- State   : Active( flags 0 ) - Purchased : X in "XX", Complimentary  
- Apps    : 291480,  (1 in total)  
- Depots   : 291481,  (1 in total)

http://steamdb.info/app/291480/subs/