I'd like to print the top layer of my EAGLE PCB so I can check wether all the components fit as they should. Obviously, the dimensions should be the same as if manufactured. What is the best way to do this?
You can check the answers on this related question: Related question
Pretty much boils down to this: You can print the board design directly or as pdf. However a lot of printers, pdf renderers automatically scale the image or fit it to the page. Make sure you have the right "scale factor" or the "actual size" options enabled and you should be good to go.
EDIT #2: Ground fills
If you want to remove a ground fill, after using ratsnest. you can use the rip up tool. If you select the ripup tool and click on the dotted outline of the layer the filled polygon is on the fill will revert to just its dotted outlines. if you ratsnest afterwards the fill will return.
You´ll have to export it to a pdf file, just like almost(if not all) all pcb design softwares have available. If you´re using corrosion and heating processes and want the top layer to be printed then you have to export the pdf with the mirror box checked, otherwise you´ll end up messing up the whole circuit.
Done that, you have to print the traces, top and board edge using a glossy paper so you can later apply heat.
Tighten the glossy paper with some tapes on the board you have.
Now you´ll have to apply heat straight on it, which if it´s a homemade project you should propably use an iron, given the fact I think you don´t owe any industrial press at home. It´s done so the ink may leave the glossy paper and stick to your board.
Finally you will only need to apply corrosion for about 20-30 min depending on acid concentration. Then you take your pcb, wash it and wipe off the remaining ink, which will give places to your traces at last.