twolfgang is correct.
Put a rag under the opening in the pump resevoir to catch drips and fill it till it overflows. I too use a turkey baster, but I slip a clear hose over the end to give me a little room to work. Cycle the top as far as it will cycle and fill it again. Do this till the top works properly and/or the reservoir will take no more fluid.
Note....if you are replacing fluid, it is going someplace. Look for leaks. If you are replacing a line, replace tnem all. If you are replacing a cylinder, replace the both.