Comets are made out of ice, rock, metal, dust and frozen gas, when they get near the sun, the ice turns into gas, forming the long tail, it also releases dust forming a different tail. When there way out in deep space it's so cold they're basically lumps of ice and rock, but many comets have elliptical orbits which bring the from those depths to our solar system where the sun can heat them up and turn the ice and frozen gases in to gas, the gas then floats around the comet, forming the first tail and making it look fuzzy.
The coma is the fuzzy white cloud surrounding the nucleus.
The coma is made of the evaporated gas from the nucleus, and dust from the nucleus as-well.
Halley's comet is periodic comet, meaning it can be seen from earth every once in a while, in this case, it can seen every 75-76 years. The last time it was seen was in 1986, and is estimated to revisit in 2061. Despite this regular return, the comet’s orbit around the sun like many other planets cannot be predicted exactly. This is partly due to the chaotic interaction with the planets and minor bodies (like small asteroids and rock) in the solar system.
The nucleus is the center of the comet that is made out of the frozen gases, ice and rock that let's out the gases when it approaches the sun, the gases are what form the coma, which I introduced earlier, The nucleus is also the heaviest and most compact part of the comet.
The comet also has a tail, the dust tail is made up of dust from the coma, and the ion tail is made up of charged particles knocked off of the nucleus. Ion tails can stretch for hundreds of millions of miles. Also, dust tails are the easiest to spot from earth, and even though it looks like the comet has one tail from earth, it's just that you probably can't see the ion tail.