How do you find out how many grams are in one liter of a 1.0M solution?

a 1.0M solution means that you have dissolved 1 mol of solute in 1.0L of solution.
You have Methylene Blue, which has molar mass = 319.85 g/mol
Therefore you dissolve 319.85g of methylene blue solute in water and make up to a final volume of 1.0L . You now have a 1.0M or a 1.0 mol /litre solution .
If you want to produce a 0.1M solution , you use 0.1 mol
Mass = 0.1mol * 319.85g/mol = 31.985g and dissolve and make up to 1.0L solution as above.