I know this sounds like such a noob question... but I am having a hard time understanding the basics such as AD/AS etc. I have read a few guides, though they don't typically go into detail on this and I have looked at various builds...but without understanding how this works it's pointless. I need to know how to build champions. Any advice/guides?
Alright so AD refers to "Attack Damage". There are a couple of parts to AD:
Every champion has an autoattack and autoattacks deals physical damage. Your autoattack has a 1:1 ratio with the amount of AD you get from items, runes, and masteries meaning if you have +45 AD from an item, your autoattack is also getting +45 AD.
Some champions have abilities that scale off of AD (whether its bonus/total AD) meaning the more AD items you build, the more dmg your ability deals.
Critical strikes normally deal 200% of your total AD. Getting Infinity edge or critical dmg runes will increase this amount more.
The defense or counter against physical dmg from abilities or autoattacks is building armor (your armor value represents how much you reduce the incoming physical dmg the enemy deals to you. Likewise, you can build armor penetration to deal more damage to targets that have alot of armor.
For AS, it stands for "Attack Speed". Some things to note about AS:
Attack speed has a numeric value that represents how many autoattacks your champion can deal within a set amount of time. More attack speed means more frequent autoattacks. (Note: Do NOT confuse attack speed for how fast your champion attacks. Think of your autoattack like a spell with a cooldown. More attack speed means short cooldown on your autoattack but your autoattack still has an attack animation which does not get reduced by having more attack speed
ADCs (a.k.a Attack Damage Carries or "marksmen") benefit the most out of attack speed because they usually build alot of AD and critical strike items, meaning they're able to attack often and deal alot of dmg with each autoattack.
More attack speed means you have a higher chance of getting a critical strike (assuming you have some critical chance in your build). A champion that can autoattack twice in 1 second has a higher chance of getting crits than a champion that only gets 1 autoattack per second, assuming both champions have the same amount of critical strike.
If you get alot of attack speed but very little AD, your autoattacks will deal VERY LITTLE dmg. You might attack faster but each attack deals very little dmg so in general, its better to build AD prior to attack speed. Some specific champions benefit more with building attack speed first like Yasuo.
AD is the damage your basic attacks do as well as the bonus damage of abilities that scale with AD. AS reduces the delay between basic attacks.
More specific questions could net you more specific answers...
Any ranged attacker needs some balance of both.
Auto Heavy Champs: These champs rely heavily on auto attacking. While several key AD items are required 
they can benefit more from attack speed. 
Champs like Vayne 
for example auto attacks to proc her main source of damage.
Castable Champs: Some champs can cast abilities which have heavy ad scaling. These generally include melee bruisers who are looking to cut through opponents with heavy damage 
or ranged attackers with heavy scaling ad skills 
Lastly there are Sheen users, generally champions with castable abilities that scale off AP. These champions like to cast a spell and then auto attack to proc Sheen. (
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This board was made to answer noob questions! It looks like there are already a couple good responses explaining AD and AS, but if you want to develop a stronger understanding of the mathematics and statistics used in League, the League wiki is an excellent resource. I found it particularly helpful in working out the importance of penetration items on damage dealers, and for understanding why my unstoppable duelist 
kept losing fights to some punk with a spear 
. The champion pages detail the scaling on each ability, so you can work out for yourself which items and statistics will work best for a given champion in a given game.
One thing to note about attack speed is that it has a maximum value of 2.5 attacks per second. I have seen some new players fall in love with champions with high attack speed, such as Tristana 
, and build five attack speed items to maximize their damage output, not realizing that, though they built 2.9 AS, the hard AS cap prevented them from ever actually attacking that quickly. Of course, they would have been doing more damage over time if they had built for AD and crits as well as AS, but that can be considered a matter of preference even if it is a mathematically simple choice.
Feel free to ask me more questions or add me in-game, as I enjoy helping new players learn to play (and ward). I also have a level six account for playing with new folks without pitting them against players of my level (I use champs I am not good with on that account so I don't ruin games with my masterful 
play). For context, I am an unranked support main with experience in every role.
