Basement ceiling drywall seams cracked

Probably the best way to fix it is with something called a "curved" trowel.

A curved trowel looks just like an ordinary 11 inch plastering trowel until you sight along it's edge or set it down on a flat surface. Then, you notice that the trowel arches up, being about 1/8 inch above a flat surface in the middle. Since you hold the trowel at a comfortable angle to the wall or ceiling when using it, a curved trowel allows a total newbie to spread a perfectly symmetrical mound of joint compound about 5/64 of an inch thick in the middle. That's plenty thick enough to cover fiberglass mesh drywall joint tape, but not thick enough to result in a visible "bump" on your ceiling even if you have ceiling mounted light fixtures.

You should be able to buy curved trowels at any home center. Also, any place listed under Plaster & Drywall Supplies in your yellow pages will sell them in both standard 11 inch lengths and a longer 20 inch length.

You should be aware that using a curved trowel eats up a lot of joint compound, so be prepared for that. And, of course, if you're using a premixed mud out of a bucket or box, thin it with water to make it easier to work with. And, finally, work with a light shining at a sharp angle to your workspace to exagerate the roughness of your work. When your work looks "OK" under such critical lighting, it'll look great under normal lighting. When it looks great under critical lighting, it'll be perfect under normal lighting.