Although you will never be able to remove every tiny air bubble you can remove the majority without a vibrating table.
It helps to leave your water over night or longer before you add it to your cement.
If I am making a stepping stone or any ornament that is relatively flat, I pour the concrete mix into the middle and jiggle the mould around so the mix works its way to the outside pushing out any air as it goes. If it has a casing I then bang it gently onto the ground and then working my way around the mould I lift up one edge and drop it in a type of rocking motion.
For those moulds that are not flat I squeeze and tap around the mould especially areas likely to get air trapped ie: feet, chins anything that sticks out. I then put the mould between my knees ( you need to sit on a chair for this) and shake my legs, holding the mould with one hand you can continue to squeeze as you go. Continue until you do not see anymore bubbles surface.
For larger moulds tap around with a hammer or place an electric tool against the mould to vibrate the bubbles out.