Just a quick note I have bolded every item.
You will always start with Spellthief's Edge and Health Potions it is up to you if you want to spend or save 50 gold. I you are more aggressive you may want three but you can get by with two. The second item that you will build is based how you are doing in lane. You could go Dark Seal into Mejai's Soulstealer if you are winning. If you are losing your lane go straight to Death Cap. Once you know you will get Deathcap on your next recall you should start to build based on who is the most fed on the enemy team. If your mid has been feeding to a mage you should build Wit's End. I usually end up building Frozen Heart because I play with a really good friend mid laner. After I have finished my second item I grab Boots of Mobility, and then on to another ability power item such as Nashor's Tooth or Void Staff. After My second ability power item I grab the counterpart to Wit's End or Frozen Heart. After that you can build just about anything you want.

Resolve is the way to go with runes. I find that Grasp of the Undying is good with Bard because hitting an enemy with a meep also counts towards Grasp of the Undying. If you can land the stun it works great.

Font of life is a small heal for you and your ADC.
Conditioning gives you extra defense so that you can focus more on AP
Revitalize find is slightly better than Overgrowth because Overgrowth just does not give you enough health to be worth having.

I chose Inspiration as the second rune because it has some useful utility.
Free boots is really good and it gives you an extra 10 passive movement speed.
I really like some extra cooldown so Cosmic insight it is.

Caretakers Shrine is very key at the start of the game. Help the jungler out at the start by planting it while you help with the first jungle camp plant as many as you can at the start of the game around the first camp your jungler is taking.(Max is three) You should get two chimes as you are leaving your base. Be sure to collect these because you will not have much to do at the start. A third chime comes really close after them. Be sure to collect all three.

The Laning Phase is tough on Bard. Collecting your chimes and not losing any XP is hard. Chimes provide some XP, but it is not enough to even be worth leaving your lane to collect them. Instead collect your chimes when the enemy carry is dead or returning. If you ever get low on mana collect a few chime to refill it. Bard's Damage is very good early game IF YOU HAVE MEEPS so try to poke WITH MEEPS as often as you can. Having a support item means that you do not have to last hit minion. Last hitting is actually bad for you slowing down your passive. Always have one of your Shrines Charging during laning for your carry and use potions to heal yourself. Your Summoner Spell heal is a last second save for you or your carry use it wisely.

Bard's Magical Journey is one of his best due to the mobility it brings you and your team. Using it to scare off you enemy laners even if it is fake is really good. It also can provide really good ganks. When you level up to three you should start faking your enemy out and throwing it on a wall from within the jungle and then not even using it or not ganking with it. Later on have your jungler come to a spot and put the portal on it then mosi back to the lane like you always have when you fake then as your enemy get used to the portal just before it closes you jungler can jump through and you can have a good gank. Magical Journey is also a really good way to bypass a tower and finish an enemy. Using it to escape is a little trickier as you should use your Cosmic Binding to stun any enemy that tries to follow you through your portal.

Cosmic Binding is one of your main sources of utility. Stun an enemy and then poke at them. Do not be to afraid because if you use your Shrine's you will almost never dent your health. Landing your Q is really important even if it does not stun. It has a slow effect that you can use to escape or your carry escape. Do not miss this it is so key to playing Bard. I have missed these and it always ends badly. Stunning through minions is hard but once mastered can be really good. The range on your Q extends when you hit an enemy so you may Unalive someone that is hiding in tower range or beyond.

Bards Shrine is really useful due to the large amount of healing it can do full charge. The ten seconds that it take to charge is kind of long but also can make very noticeable difference in a heal. During the lane phase always have one or two heals charging for your carry. Try to heal yourself with potions only and leave your shrines for the carry. Shrines can really help out your Jungler at the start so stack as many as you can at the first camp your Jungler takes.

Bard is really powerful late game and has a insane passive that allows you to deal lots of damage throughout the entire game. His utility is amazing once you can aim and land stuns through minions and that Ult that put the carry out of business while you and your team wreck the other four players. Bard Magical Journey works much better on while your base is at the bottom but still works for top base. Do not miss your stuns they will determine if you win or lose a fight or if you live or die. Gather as many chimes as you can but do not miss XP. At 15 Chime you get and area of effect which increases at 65 Chimes. At 100 Chimes you will have the max number of meeps. Land a stun use a meep to auto attack with and you get an easy 30 gold witch helps you help your carry get ahead.

Bard is really powerful late game and has a insane passive that allows you to deal lots of damage throughout the entire game. His utility is amazing once you can aim and land stuns through minions and that Ult that put the carry out of business while you and your team wreck the other four players. Bard Magical Journey works much better on while your base is at the bottom but still works for top base. Do not miss your stuns they will determine if you win or lose a fight or if you live or die. Gather as many chimes as you can but do not miss XP. At 15 Chime you get and area of effect which increases at 65 Chimes. At 100 Chimes you will have the max number of meeps. Land a stun use a meep to auto attack with and you get an easy 30 gold witch helps you help your carry get ahead.