I do quite a bit of wood work, including large glue-ups of flat surfaces.
1) To achieve very thin but even glue coverage, use a
squeegee. It can also be done with a wide foam brush, but to get a razer thin layer a squeegee is quite easy.
2) Use a roller, such as the types used when applying veneer or edge banding. Work the roller radially out starting at the center. This will help eliminate bubbles and ripples.
3) Some additional advice that may come in handy. Applying any type of paint, glue, stain to only one side of a surface can introduce cupping of the workpiece due to uneven moisture absorption. The general rule is that you should always do the same thing to both sides of a workpiece.
4) You will need to place the board you are gluing to between at least 2x3/4" boards on bottom and 2x3/4" boards on top. You will need to clamp these boards down using cauls so that there is sufficient pressure in the middle. There are two ways to make clamping cauls. The first is to use a hand plane on the boards that are the cauls. Another method is to place thin strips of increasing height on the boards as you get closer to the center. Generally for a 24" board around 5 strips is sufficient. The outer strip might be 1/16" thick, the next two 1/8", and the inner-most 3/16".
Basically, read up on how to apply thin veneer, which is typically 1/42" thick (which is 0.6mm). Tommy Mac host of PBS's Rough Cut likely has an episode or two where he does this.
Hope this helps.