F = m * a. = 1 kg * 9.8 m/s^2. =9.8 Newtons. So to counteract the weight, or in other terms, the force of gravity on the mass, we need to apply an upward force of at least 9.8 Newtons. As to how much work is done, we can use one of the work equations, Work = Force * displacement. It would look like.
To lift it directly, you need to know the force per mass of the gravity. On Earth this is 9.8 N/kg, but on the Moon it is only 1.6 N/kg. Basically, just multiply this value by the mass e.g For the Moon: 1.6N/kg x 100kg = 160N needed (well that would keep it balanced and you just need a little extra to lift it.)
To lift an object of any mass takes an upward force greater than its weight. To keep it suspended takes a force equal to its weight. The weight of a 1 kg object in a 1 g gravitational field is 9.80655 newtons. For quick back-of-the-envelope calculations, call it 10 N. How much force is required to lift one kilogram?