Radiant Fountain reads "{T}: Add {1} to your mana pool." Does this card alone produce a total of {1} or {2}?
Basic Land cards produce mana when tapped. So, either
{1}.
You will only get one colorless mana added to your mana pool when you tap Radiant Fountain. Lands do NOT have an automatic built-in ability, only lands with one of the basic land subtypes do. Radiant Fountain does not have one of these subtypes (Mountain, Forest, Plains, Island, or Swamp).
Even if it did have one of these subtypes, you would still not be able to tap it for 2 mana. Say you have a Radiant Fountain and a Urborg, Tomb of Yawgmoth in play. Radiant Fountain now has 2 abilities:
In this case, you have these 2 separate Tap abilities, but you can not tap once to get both mana. You would have to choose which ability you wanted to activate by tapping the card, and you would get just 1 mana whichever one you chose.
There's no such thing as lands producing mana by default. They only produce mana according to the abilities given to them. It's entirely possible to have lands which generate no mana at all: consider Dark Depths, for example.
You're probably now thinking "how do Islands work then? They have no abilities at all." However, basic lands — Islands, Mountains, Plains, Swamps and Forests — all implicitly, because of having that basic land type, have an ability of the form:
{T}: Add {color} to your mana pool.
Where {color} is blue, red, white, black or green depending on the type of land. So if a land is a Forest, being a forest implicitly means it has the ability:
{T}: Add {G} to your mana pool.
Lands of more than one basic land type, such as Steam Vents which is an Island Mountain, implicitly have this ability for each of their types, but you can only activate one. Hence the reminder text at the top of the card's description:
({T}: Add {U} or {R} to your mana pool.)
It really has these two abilities implicitly:
{T}: Add {U} to your mana pool.
{T}: Add {R} to your mana pool.
But tapping a card doesn't mean activating all tap abilities on it. You pick an ability (just one), and tap it to pay the cost of that ability. When a card like this has two tap abilities, that limits you to only being able to activate one at a time. (Unless you can untap it somehow, such as with Kiora's Follower.)
Radiant fountain has no basic land types (it's not an Island, Forest, Plains, Swamp or Mountain). It has exactly one mana ability, which adds 1 colorless mana to your mana pool. That is the only mana it produces.
When tapped, Radiant Fountain will add only one colorless mana to your mana pool.
A player only has one mana pool which holds all mana produced for that player, whether from a land or an ability on a different card type.
This effect is the same as the intrinsic ability of basic lands which add mana of a specific color to a player's mana pool. Tapping Radiant Fountain and a Forest would give you {1} and {G} mana in your mana pool giving you enough mana to play a Runeclaw Bear for example.
