When a host approaches, four "petals" at the top of the egg open up, and a facehugger launches out. The Space Jockeys used an anesthetic mist to put them in suspended animation for safe handling.
When no host approaches, the egg develops several tendril like roots, probably for nutrient absorption similar to plant organisms, to help it sustain itself until a potential host appears. Another theory is that the tendrils are used for communication between eggs, like the synapses in brain cells, to inform other eggs of host approach. It is not known if an empty egg will create more facehuggers. The Director's Cut version of Alien and the AVP SNES game showed that a human can be turned into an egg. However, the cut scene in Alien was a scrapped idea, and should not be considered entirely canon. This was most likely in the game by mistake.