I don't really understand the mechanics of attack move, ie what will you attack (closest? prefer champion?), and when do you attack after clicking?
If you attack move, your champion will attack the closest target, the instant it gets in range or becomes visible. Once it's attacking a specific target, it won't change targets even if others get closer, unless you manually override it.
Attack move is generally useful only for making sure you start dealing damage as soon as possible. As soon as you're actively engaged in combat, manually selecting targets is the better option. Attack moving into brush, for example, will mean that you automatically get an attack off if the enemy happens to be standing there, but then you should really (quickly) analyze the situation and decide how to continue, giving your own specific commands.
The two links below first of the video explains Attack move or stutter stepping and why you want to use it in lane. The second link will guide you through the process of remapping you're middle and left click mouse button so that you may make full use of them instead of using shift click you will use you're mouse clicks which is far better and less tedious(Unless you have become accustomed to this)
Attack-Move or stutter stepping . is a mechanic that can be used by all champions in the game however it is very useful and important on ADC or Marksmen (season 3&4), the reason behind this is efficiency first. League of legends is all about time so normally in lane when you move to attack something you would use move click then attack, this can cause you to miss a CS(creep score) which will get you behind in lane if your lane opponent is able to get more CS than you, there by able to itemize better than you. This is where stutter stepping or attack move comes into play with this you will never not attack, you're champion will move to the desired target and attack however, you have to be wary of creep aggro (when the minions focus and attack you) so be sure you will be able to get you're AA(auto-attack) off and quickly retreat this is called harassing your lane opponent.
Attack-Move in Bottom or ADC-Marksmen/support lane
Champions who excel in this are Caitlyn ,Jinx, Tristana and well to be honest any ADC-Marksmen can do this very well however I mention Caitlyn , Jinx and Tristana first as they have very long range. you have to use this range to you're advantage as often as possible to keep you're lane opponent low on hp(health points) there by forcing them to miss CS for fear of getting killed or dropped lower in health by you and you're support or getting ganked and killed. I must also mention that if you are able to master this you can potentially drive out your lane opponent and get a lot of free farm and exp for you and you're support depending on the trinket you're support has, the new trinkets are:
Another "thing" you may use attack-move for is of course chasing an enemy that you are confident you will win against in a brush or where the fog of war denies you vision. Be very careful when you do this as you may be getting baited into a bad position so always take note of the map for any missing enemies ESPECIALLY TEEMO and his shrooms. Finally in a team fight or when you are chasing an enemy it is optimal to use attack move as it ensure you are constantly dealing damage. Be wary of "thorn-nail (returns a % of the physical auto-attack damage or ON-hit damage(GangPlank Q,Ezreal Q, abilities that are treated as auto-attacks) you are dealing to the enemy you are attacking back to you), Rammus W(similar to thorn-nail passive), Annie E(deals magic damage to an enemy that auto-attacks her and gives her bonus MR(Magic Resistance and AR(Armor)), Fiora W(reflect you're AA back to you plus bonus magic damage)" AA these champions while you are low on HP can hurt you're team as you maybe dived and die or you may have to recall.
Attack Move in Mid and Top(Solo Lane)
The same rules apply however the difference here is that you maybe range or melee. Regardless the lane however if you feel you will be disadvantaged in terms of trading AA's then always purchase Dorans shield (for non mana dependent Champions) this will reduced the damage you take by a very large amount throughout the laning phase of the game, another thing you may do if you feel confident you can pull it off is you start with boots and pots this is best for when you are the harasses if you are being harassed though it may not work as well however it is a great way to sustain. In my opinion though all melee champions vs a range or AA heavy poke champion should always buy a dorans shield. This works very well VS Nidalee, Leblance, Ziggs, Syndra and such champions. However do not let them AA you when you know their Range spell is ready for use as you will take bonus damage thanks to the new mastery spell weaving(damaging a champion with a basic attack increases spell damage by 1% maxing at 3%) and Blade weaving (damaging a champion with a spell increases basic attack damage by 1% maxing at 3%) Blade weaving is not as powerful as spell weaving on Mage champions(spell casting champions) however Ziggs, Oriana and Kassidin are champions you want to avoid trading with when this passive is active as they have AA buffs.
In the Jungle
Em so this is a bit tricky first of you do not really need to worry about lasting hitting so kinda not useful however, HOWEVER. Using attack move in the jungle will help keep you're HP up any champion again can make use of this the problem though it can potentially decrease you're clear time if you use it incorrectly.