There seems to be very little in the PHB about how a Beastmaster Ranger is supposed to acquire his animal companion.
Initially we have:
Choose a beast that is no larger than Medium and that has challenge rating of 1/4 or lower….
If the initial companion dies:
If the beast dies, you can obtain another one by spending 8 hours magically bonding with another beast that isn't hostile to you, either the same type of beast as before or a different one.
In either case, where does the animal come from? Does the Ranger have to either purchase or find a wild beast wherever he happens to be adventuring, or can he somehow call a creature of the desired type to him? Does he automatically make the creature non-hostile and bond to it immediately the first time (since there is no mention of needing to do that explicitly in the initial description of obtaining an animal companion)? Is the Handle Animal skill sufficient to make a wild beast non-hostile for long enough to bond to it?
Best Answer
As you say, the last paragraph of the ranger's companion text mentions needing 8 hours to magically bond with another non-hostile beast if when the previous one dies. It is probably the same for the first time around.
As for how to get the beast I haven't found specific ruling, so it's probably up to the player to find a beast to his liking (any plausible method should work unless the DM requires anything specific), ensure its friendliness and then bond with it.
A survival or perception check to find one in the wilderness and a handle animal check to calm it should do the trick, and the ranger spell list includes some spells that could help, like "locate plans and animals", "animal friendship", "speak with animals" or "conjure animals".
The beast selection is limited by what kind of beasts exist in his environment, which is something the DM decides.