I haven't played her much, but I always go with Tear and boots first. Her mana goes quick, and if you aren't making use of her zoning than you aren't playing her strengths.
Personally, I would say Tear + Boots
Then Hybrid damage + tankm making use of AA to get damage from APless items
Glacial Shield for Mana (AP) armor and CDR
Possibly Wits end for Attackspeed, MR
Skilling Order is dependent. If the enemy isn't a super farmer/pusher, grab poke build.
QWE Q E R Q E Q E R Q E W W R W W
If you need to farm, max shield and slow
QWE W E R W E W E R W E Q Q R Q Q
That's my opinion anyways.
Masteries? Not sure. I personally Like defense on everything cause I think it's one of the best trees all around, going 9 offense for magic pen, then grabbing 6 Armor MR, 6HP/level, 30HP, 2 lee dmg a hit, Initiator, 8% CDR at 18, and then 3%HP and 10% Disable reduc.
Summoners? Despite the popular dislike of it on Dom, I role Flash every game, on every champ, especially bot lane. The jump is far enough to jump from bush to bush in an escape, or over the small sections of the walls to gain distance, or to gain distance for the last hit. Surge has potentail since she makes use of both the AP and AS, but I would argue more towards Ignite as a second, since many bot laners have sustain built in, or as a mandatory item. (Ryze, Morde, Yorick, Heim, Morg, ect. ect.)
Runes? Mpen Reds, HP Yellows, maybe CDR blues? Quints would probably be Run speed, since I recently have become fond of them.
Played a game as her bot, came out as 10/4/19. However, it should be noted that I did need a lot of help at bottom against Yorick. Now, whether the ganks were needed cause of being against yorick, or something else I can't really tell you.
Final build was AA Merc FH Wits Rylias and a blasting wand, thought the goal was a Deathcap, runes and masteries were as above.
After reviewing her Mana Costs, Im going to do skill up differently.
I will go QWE Q Q R E E E E R Q Q W W R W W
I raise Q to 3 and stop because at that point it is 60 mana a use, equal to E, only E has no mana cost increase, and gives survive ability, damage, and I believe travel faster. W is maxed last do to the amount of mana it uses. Hopefully this should keep mana levels more steady.
If this brings only limited success I'm ganna also focus a lot less on AP since she has low ratios anyway and perhaps go Hybrid / on-hit.
I had just realized this, but E damage doesn't degrade as it hits more people according to text, possibly making it the best poke. Perhaps it should be maxed first?