If you are referring to one mole of hydrogen atoms, the answer is 1.008 g.
If you are referring to one mole of hydrogen gas, the answer is twice this amount, 2.016 g.
Looking at a periodic table will give you the molar mass of any element you require. You should note that this will be the mass of one mole of atoms of that given type.
In nature, many of the elements exist in a form that groups a small number of atoms together to make a more stable molecule. In the case of hydrogen, the gas is composed of molecules in which pairs of H atoms have bonded together. These are called diatomic (two-atom) molecules. (This is also true of nitrogen gas, oxygen gas and several others.)
So, the molar mass you which to determine will depend on whether you are referring to a mole of atoms or a mole of the gas made from these diatomic molecules.
Here is a very good online periodic table you may find useful