Step-by-step explanation:
Objective lenses are responsible for the primary image formation in microscopes, they are the closest part to the object, it defines the image's quality and they determine the magnification and resolution. In an optical microscope you can usually find 3 or 4 objectives (4x, 10x, 40x and 100x) but other configurations and magnifications are possible, in the image I added you can see that.
To determine which objective you will use you need to consider your specimen's size and what are the smallest features in it, NA (numerical aperture) must be considered as well, this is the ability to gather light and it determines depth of focus (how much you can focus without change in the image's sharpness), brightness and resolution (smallest distance between two objects). You'll also need to identify your observation method (phase contrast, darkfield, fluorescence, etc) and in what medium is your sample.
I hope you find this information useful and interesting! Good luck!