In astrology there are planets. In ancient astrology they are 7 in total - Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. Modern astrology adds a few more to the already existing ones - Uranus, Neptune and Pluto. Anyone can decide for themselves whether they want to use ancient/traditional astrology or modern astrology. There is no specific way of learning astrology that must be followed, anyone can choose how to learn it. Personally I tend to use more modern astrology compared to traditional even though sometimes I tend to use traditional as well. Here is a table with all symbols, to be able to read a natal chart in the future it is highly recommended that you remember these symbols! In the beginning you can always write them down or have them somewhere where you can easily check which symbol to which planet corresponds until you remember them and don't need a cheat sheet. Until then here is one:

Each planet rules one or two signs.
Sun - Leo
Moon - Cancer
Mercury - Gemini and Virgo
Venus - Libra and Taurus
Mars - Aries
Jupiter - Sagittarius
Saturn - Capricorn and Aquarius
Uranus - Aquarius
Neptune - Pisces
Pluto - Scorpio
Keywords for each planet:
Sun - individuality, energy, power for achievements, self realization, will, integration factor in the horoscope
Moon - the soul keeping memories from previous lives, the unconscious, emotions, fantasy and imagination, purification, habits
Mercury - intelligence, studies, knowledge of the universe and healing, mediator between the higher and daily mind
Venus - love and beauty, aesthetics, love in different forms, can give artistic expression, feeling of sharing with others, social orientation and subtlety
Mars - the warrior inside of us, active energy, dominance, courage, weapon with which we fight, wanting to win/achieve something
Jupiter - gives more to the spiritual, deep understanding of the philosophical and esoteric rules, religious feeling, enthusiasm, generosity, connection with law, the truth
Saturn - wisdom, karma, justice, patience, accountability, accuracy - things that can be developed in the material world
Uranus - higher knowledge, connection with the universe, idealism and love of freedom, destroying all borders that don't let people connect with each other, especially when connected with electricity or the internet
Neptune - inspiration, universal love with no boundaries, illusions, spiritual experience/feeling/talents, empathy
Pluto - full transformation of the ego, the topic of death and rebirth, psychic powers/abilities, getting over things that stop us mentally/unconsciously
Another important thing for every astrologer is to know how long a planet spends in each sign. This can be very helpful when working. Here is a list of how long each of these mentioned planets spend in one sign(approximately):
Sun - about 30 days in each of the 12 signs
Moon - 2 - 3 days
Mercury - about 3 weeks
Venus - 5 weeks
Mars - 8 weeks
Jupiter - 1 year
Saturn - 2.5 years
Uranus - 7 years
Neptune - 165 years
Pluto - 284 years
We all have each planet in our natal charts. These planets are mostly in different signs but some can be in the same sign. If 4 or more planets are in the same sign then we say that there is a stellium in the natal chart. A stellium can mean "the main focus" in a chart. The house where there is a stellium is important as well. It's important to check which planets are part of it. Not everyone has a stellium in their own chart(for example I don't have any stelliums). The characteristics of the specific sign and specific house become more dominant when there is a stellium. A person might be doing a lot of things that are related to the main themes of the sign/house without even knowing, doing something subconsciously in their daily life.