Yes your fingers will get all greasy. Replace the slide
tube.
With your fingers wipe off any excess grease that
squeezes out after you insert the slide. Use this excess to
put on the next slide. Do the same thing with the next
slide.
Oiling "fast slides"
These are usually the 1st and/or 3rd valve slides. On many trumpets
the 1st and 3rd valve slides are designed to be a fast moving, fine
tuning slide. This is why you have a finger ring on it, so that you can
move it while playing with your finger. On better quality trumpets
these slide are made to move freely and if you want to retain this
function then you do not put grease on it, since grease will sow it
down. Instead you put oil on it. Remember anything you want to
move fast on a trumpet you put oil on it, anything you want to move
slow or leave in a certain position, you put grease on it. So if you
want to retain the quick movement of the 1st and 3rd slides then put a
drop of oil on each slide tube of the 1st and 3rd slides every time you
oil the valves. Always press down on the corresponding valve to
move the slide and when spreading the oil around since there is
vacuum inside the trumpet.
NOTE:
If you are a beginner or have only played for a few years, chances are
you will not be using your 1st and 3rd fast moving, fine-tuning slides.
Therefore, its a good idea if you grease them and just make them into
slow slides, since you are not using their fast slide capabilities
anyway. The choice is yours what you want to do. Sometimes its just