Question about mana.
First, you cannot have mana on the battlefield. Mana is something that only exists in your mana pool after being generated (usually by tapping a land, though there are other things that can do this too like Sol Ring or Dark Ritual or Elvish Mystic). Now for your questions:

You pay for a spell when you cast it, so if you are casting a Gray Ogre you would need to generate 3 mana (1 red and 2 of any kind). You would generate this mana by tapping lands in most cases.
You do not need to pay any mana for a creature to attack (unless an effect like Propaganda requires you to).

From the MTG Quick Start Guide
Casting spells:

You must pay mana for each of these symbols in order to cast Shivan Dragon. The symbol {R} means one red mana. The symbol {4} means four mana of any kind. So you have to pay two red mana and four mana of any kind to pay this cost.
When you want to pay a mana cost, tap (turn sideways) the necessary lands on the battlefield. This shows that you’ve used those lands to produce mana.

Attacking:

During your turn, you decide which of your creatures, if any, will attack. You can’t attack with a creature if it’s tapped or if it entered the battlefield this turn. You have one combat phase in the middle of your turn, and all the creatures you decide to attack with attack at the same time.
Once you’ve decided which of your creatures are attacking, tap those creatures. Your tapped creatures, like your tapped lands, will untap at the beginning of your next turn.