There have been changes and other rune alphabets as time has passed. As well as additions or subtractions to the original Futhark set. One of the most commonly seen and used is the 25th blank rune, also called Odin's Rune, that is, essentially, a wild card rune that means the possibilities are endless or anything can happen. This rune, or rather lack of one, was an addition around the 18th century and not a part of the elder Futhark. Some people choose to use this rune, others choose to leave it out and use it as a replacement if another rune stone gets lost somehow. The runes are thought to have dated back to around 200 B.C. but some sources may state their origin even earlier than that.
The word Rune itself also literally translates to both "letter" and "mystery". These letters are able to be applied in many ways, from being an actual alphabet to write down and document things, for use in spells and blessings, to being engraved or carved to consecrate ritual tools. The sheer versatility of the runes themselves and power behind something seemingly so simple is what attracted me to learning about them in the first place, and continue using them now.
The runes are grouped into 8 sections of 3, known as aett/aettr. The top row is known as Freyr/Freja's Aett, middle known as Heimdall's Aett, and bottom row as Tyr's Aett. Sometimes during a reading the runes may appear upside down or "merkstave" (Also called reversed runes). Merkstave runes do not imply an opposite meaning of the original rune, but rather a usually darker or more negative meaning behind it. The runes also come in pairs of two across, and are more-or less opposite meanings. (Example: Cattle as compared to Wild Ox)
So, without further ado, The Runes.
Freyr/Freja's Aett:
Fehu - Cattle - A rune of wealth or material gain.
Uruz - Wild Ox - Strength, boldness or vitality.
Thurisaz - Giant - Poetic justice, destroying evil forces.
Ansuz - Wise God - Wisdom and instruction.
Raido - Quest - A journey that must be taken, a spiritual awakening.
Kenaz - Torch - A goal or a solution to a problem, a light in the dark.
Gebo - Gift - A sacrifice or offering, assistance.
Wunjo - Glory - Joy or the fruits of a sacrifice, recognition or reward.
Heimdall's Aett:
Hagalaz - Hail - Chaos and destructive force, something out of our control.
Nauthiz - Need - Necessity, a will to keep going, suffering.
Isa - Ice - Superficial beauty, illusions, an elusive dream or goal.
Jera - Harvest - Transformation, reaping what you sew.
Eihwaz - Yew - Dependability, something or someone who will not fail.
Perthro - Apple - Abundance and satisfaction, sexuality.
Algiz - Defense - Warding or warning of evil, a guard on watch.
Sowulo - Sun - Judgement, decisions, and actions to be made.
Tyr's Aett:
Teiwaz - Courage - Upholding of truth and final arrangements.
Berkana - Birch - Fertility and desire, a creative spirit.
Ehwaz - Horse - Rapid progress and advancement.
Mannaz - Man - Foresight, intelligence, an expression of purpose.
Laguz - Water - Going with the flow, creativity and emotion.
Inguz - Fertility God - Family and child growth, simple virtues and honest work.
Othila - Home - Land or property, accomplishments and skills in life.
Dagaz - Day - Clairvoyance, a period of study, gaining answers.
Keep in mind that sometimes depending on the rune spread you are doing, the meanings of the runes aren't always to be taken literally. In fact, most times they aren't. Sometimes reading them takes lots of time and thought as to how the specific rune relates to a person or question at hand, or how they can relate to the other runes around them.
There are many ways to do Rune Spreads, or you can make your own. The easiest spreads to do are one, two, or three rune spreads. A one rune spread is just that. It isn't the most accurate or concise, but a bit like pulling out a daily Tarot card. It only tells you the overall feeling or general concepts of the question. Two runes deals with "That which is" and "That which will be". The Norse didn't quite have the concept of past, present, future. Instead "That which is" is a combination of both past or present and "That which will be" is the future. A three rune spread however, does deal with past, present, and future and reads about the same as a Tarot spread might.
There are also five, seven, and nine rune spreads, and even more if you factor in that everyone has their own way of reading them or coming up with their own. If you want to do bigger spreads if you feel like you've already mastered reading the smaller ones, I'd suggest looking up some more spreads and ways to cast them. http://www.therunesite.com/casting-layouts-and-spreads/ is the site I would personally recommend for this.
Please keep in mind that there are far more ways to interpret the runes than just what I've stated and more ways to use them than just for reading your future, such as in sigils or combining them to make a more powerful spell.
Good luck and best wishes in all your future Futhark endeavors.