There are two ways to remove an LP from it’s inner sleeve: with your left hand (if you’re right handed) tilt the LP in it’s sleeve and let it slide out, an edge of the LP coming to rest in the palm of your right hand.....or with that right hand reach into the inner sleeve and, without touching the playing surface of the disc, put three or all four fingertips on the label and guide the LP out of the sleeve.
Once you have the LP out of the sleeve and balanced on the fingertips of your right hand, put down the inner sleeve and with your left hand now free put the edge of one side of the disc into the palm of that hand and put the fingertips of that hand onto the label. That will allow you to then let the edge of the opposite side of the disc come to rest in the palm of your right hand, such that you no longer need the fingertips of that hand to support the LP, nor the fingertips of the left hand. You will now have the LP held between your two hands, opposite sides of the disc in the palm of either. Balancing the disc in the palm of your left hand, move the fingertips of your right hand to the edge of the disc, then the fingertips of your left hand to the edge of the opposite side.
You will now be holding the LP in the exact way you need to place it on your table’s platter, all without having touched the playing surface of the disc, which you should never do. If you accidentally do (we all have), hold the LP up to a strong light source with one hand, locate the fingerprint left behind, put a drop of cleaner on the spot, place the LP on a clean surface (your table’s platter, for instance), and remove the finger oils with your brush or cloth.
I went into excruciating detail for the sake of clarity, which makes it sound much more complicated than it really is. It will soon become second nature.