How can we identify what the distribution is?

The only way to know the distribution of a variable is to assess whether the process of generating the data fits a certain distribution. Many of the processes that you can analyze have been previously analyzed by academia and that can help you a lot. Examples:

2) Stock prices are famously known to follow a lognormal distribution. As you can see from the photo below - there is a low number of low values, high concetration of say 3% return (completely arbitrary number), and the tail to the right is steeply becoming thinner and thinner, until it almost touches 0. This shows that many people earn low return, and very few companies earn a high return
3) Throwing a die follows a Uniform distribution. All outcomes are equally likely (1,2,3,4,5,6). Drawing a card from a deck is such an event, too. There are 52 cards in a deck, and the probability of drawing one of them is 1/52

4) Radioactive decay is more or less known to be a Note that the Poisson can apporximate a lognormal and a normal distribution, depending on its parameters. And so on.
There are hundreds of known distributions, however, only a few of them are very common for different processes.
The world is random, but in a predictable way.