Sorry for my lazy writing, I'm new to mobefire, so here's my worded explanation...please give feedback!
Tl;dr? Just read the items (and summoner spells).
Examples coming soon.
For those noobs that don't know, always keep the minions waves on your half of the lane, making room for your jungler to gank. You can achieve this by last-hitting, only attacking if its a killing blow, and pressing the s key to cancel your attack (if you throw the attack, and it isn't a killing blow, you'll lower its hp and then one of your minions will take the kill, press s, let minion attack first, then you last hit), you can use the "rests" for dodging harasses and harassing the enemy adc (but watch your mana, using spells for last-hitting is important too!)
Always max out offensive spell first (usually), and escape spell last (no point of making escape deal more damage). The only exception is Caitlyn, where you get snares first (use first 2 minutes placing them for escapes/prevent ganks later). Use the offensive spell as your "other basic attack", last hitting minions in huge waves or when there's two minions of equally low health. Don't be afraid to use your ult to "ks" (unlike Karthus)...carries need to be fed!
You'll need flash for sure, really helps you get away from the enemy support than cc'd you, before the enemy carries lands free hits on you. Good for catching kills and diving too.
Your spell can be ignite, heal, cleanse or barrier. Ignite is really good for those early kills, and with the mastery, you get more ad...making you last hit better. Heal is for those that can really harass, but get harassed instead (Ashe), and so you need to heal to stay in lane. Cleanse is for those "life steal towers", dealing a **** load of damage, and when you get attacked, you just lifesteal it back...but if you get blinded, stunned...etc. you're pretty much screwed and you'll quickly be wiped (no escape spell) (e.g. Vayne). Barrier is a pretty derpy spell, and the only adcs I really get them for is Corki and Caitlyn, but I think I prefer heal more. Ignite is for the burst adcs, making you even more bursty, coincidentally, these champs happen to the be the 6300 IP carries...so it'll be easier to remember for you. These champs also have decent escapes, so no need for defensive spell, or can fight it out, ignite works really well on champs with damage over time (e.g. Twitch).
You can either start doran's blade or boots % 3 pots, but I always start blade; you have a support to heal you, it helps you more with last hitting and what if you run out of pots, with blade, you can just farm and get your hp back. The only problem is during the first fight, the enemy can easily get away (and many make the mistake of flashing after them). I find that with blade, I can always farm until I can at least get my bf sword. The next big item is bloodthirster, you can little items before that, such as boots, avarice, vampiric...etc. but nobody what, bloodthirster first (don't be a noob and rush infinity edge), you get useful lifesteal, and at max stacks, it gives more ad than ie, and what's the point of crit if you'll just die from the lack of life steal during fights? Not to mention, ie costs more. You're next item would be a item that builds off cheap items, such as stattik shiv, trinity force...etc. unless you get really fed and can afford ie (always but the most expensive item you can after recall (if you can actually build it into something useful later)). I like getting stattik shiv on all non-burst carries, the avarice blade is really useful and it makes poke much easier (I don't even have to hit them!), very essential for weak carries like Ashe, it's also good replacement for the now-useless phantom dancer (the crit, and it gives more movement). Black cleaver is also really good because physical spells apply it, you can also get last whisper (really helps ad spells...so get for sure if you have 2 or more). For defense, you can get guardian angel, scimitar or banshee...pretty when to get each. If you're going for banshee, you might as well grab the catalyst...really nice if you don't handle your mana well.
Seals: Flat armor
Glyph: MR per level
Mark: AD or armor pen.
Quintences: Health or AD (or even armor pen.)
I just roll with hybrid pen. marks and quintences, works for all champs.