Your laning phase should be extremely easy if you're playing well, predict their movement and move around while pushing your Q towards the enemies, while also trying to dodge enemy skillshots. After you land it, auto attack once and move away with your W so you proc Electrocute/Phase rush. If you have Electrocute, stop the trade, if you have the Phase Rush runepage, continiue the trade because of the Bone Plating and the movement speed Phase Rush provides

Post 6, you should wait for your jungler to gank you and make sure you land the full W.

This changes based on your laner. If they're an aggressive laner like Yasuo/Zed, stay back and only poke, however if you're into an Orianna/any poke mage, land your Q, full W, R them and ignite, that should be enough damage to kill them if you traded well enough during the game.

Farming with Asol is actually quite easy when you get used to it, he practically afk farms. Stay on the bottom side of the minion wave to hit them with your passive/W more consinstetly. Hit melee minions with your Q, the whole wave with W and auto attack the cannon to push, as Asol pushing is easy and reccomended into most matchups

Roaming with Asol is also incredibly easy, his E range on lvl 1 allows you to go behind the enemy adc and support, from there you can cc them with your Q or R. Try to roam as much as possible, especially if you're into a bad matchup, which there are plenty of for Asol.

Using a big Q with E is nice, though difficult to hit consinstetly, so I recommend that you use your E to get behind them. It's better to have a guaranteed 0.5s cc than to have a chance to hit a 3.5s one.

Asol is more of a burst mage since his W was reworked, not nearly as much of a battlemage as he once was. So naturally, hitting every single instance of your W is important, since it's on a duration now, not a toggle.

Positioning will take hundreds of games to perfect, dodging, hitting multiple enemies with your abilites and lining them up for your R-Q combo is tough. You can either burst enemies of high importance and impact on the game or sit back and damage everyone slowly, depending on your build, team and the enemy team alike.