A pretty standard thing is to put all the creeps in the wave low HP with autoattacks and then grab all the CS with an AOE skill, like Orb of Deception.

Couple of options.

Buy your standard items in the Practice Tool. Since no one is going to gank you or contest you for the farm you should aim for perfect CS.

You can try a couple of things to help if you are really struggling.

1) Go 10% attack speed in your runes (potentially a legit strat in a matchup where you can auto your opponent a lot)
2) Buy a longsword

But probably just get comfortable with your chosen champion's auto attack animation without artificial aids. Some characters have ridiculously bad AA animations (though Riot has improved some of the worst offenders).

If you have buddy you can create a custom game (Butcher's Bridge works pretty well for this). And have them throw skill shots and auto attacks at you while you try to CS. Aim for about 80 cs/10 min.

Then step it up to normals and try it again vs a variety of different champions. Again aiming for around 80 cs/10 min.

Also some champions have abilities that basically do 1 AA worth of damage (Vladimir's Tides of Blood for instance when uncharged. You can use that to get 1 AA of dmg on the caster minions, then let them take a tower shot and then finish them of with an actual AA.

So learn which abilities will allow you to maximize your CS under tower.

You also need to watch the projectiles coming off the caster minions as you may need to AA a minion that is getting focus fired instead of another minion that isn't getting focused.

Eventually you should get to the point where you don't even look at your character model at all so you can pay attention to the map.

gl