This is how i play heimer usually solo mid.
Clarity : You re gonna need tons of mana early game and clarity is awesome to recover mana to place new turrets and throw some rockets..try to use it as soon as its up and u re low on mana so it coolsdown
Teleport: You can tele to your turrets..u dont want to stay too much time away from em or they get killed .. Plus one main thing of heim is he grows really fast so u wanna take advantage of that and dont lose any sec on the lane.
mana crystal: Get this crystal so u can build up tear of godess after..This will give u nice mana with the mana pot and health pot u should be ok till your fist trip back.
1st trip back MUST get tear ..and maybe pendant..if u got money get the chalice..This item is optional just buy it if the other guys is destroying your turrets to much and u really need extra mana, if keepin em up is not a prob...focus on arcangel and your boots.
After you get arcangel and boots...Why swiftness and not sorcerer..u need to move alot if u solo or even if u not...it can help to runaway and to chase enemies to rocket to juke.. all items are ap..u dont need sorcerer.
When u get archangel build up your rod of ages starting from the catalyzer..Nice mana and health plus a little ability power that comes from the archangel passive
Buy rod as soon as possible to max the cap.
MEIAS.. u re always assistin and killin get it..awesome and cheap.
Rylais: U slow ppl when turrets hit em or rockets...end of story is good and 500 health its enough for u to survive those damn gangs cuz u ownin mid so bad.
And zonyas is just pure ownage..by the time u get zonyas and u got meias at around 10...your rockets just get 40% of health or so on most champs unless they tanks...u re gonna be killin alot with rockets in team fights..and your nades do serious damage.
HOW TO PLAy??
At beginnin go mid or lane place a turret..by the time minions come ull almost have full mana to place another if it gets killed... Skill order depends on game..u playing ranged player? get a nade to blind and stun..u playin melee? get rockets to get em away..its always nice to have both but remember not to spam that much early game cuz mana goes away easy...After you get tear and chalice or arcangel is spammin time and u should be spammin get some manaa pots if u going low plus u got clarity.
Try to place 2-3 turrets all the time and continue to push with your nade..u will get that turret eventually with help of minions.
RUNES: Magic penetration + Cooldown...yellow runes i dont care..just use dodge health watever u like better. It doesnt matter if u dont MAX cd..why? cuz it ll be probably 1 sec cd u miss and u should get golem buff anychance u get Heimer is awesome at jungling so go and get golem buff when its up.. Remember heimer has health regen as passive so dont tele back just cuz u ow health ..Use a pot stay back for a while and start replacin turrets.
Heimer is a great killer and pusher and most ppl underestimate his turrets and will probably go all to get u when they see u..u just rocket nade on yourself if hes melee and ulti..hell be dead in a sec and be raging that he got killed by a heim.
On team battles throw your nade when ppl is all gather around and it will damage most of the team..ROCKETS? well they might be minions around so just spam em..1st maybe kills minions but after that minions are gone and u will hit a champ or 2 and do some damage...Turrets? place em In the middle of everything why? u will get assists and help the team alot..Remember when u place it it has 6 second atspd increased..beleive me on taem fights the last thing the other guys are worried is a bout a fkin red turret shooting stuff ..they will be trying to get some1 else or u directly so just throw in the turret nade rocket and gtfo until u got cd your abilities... Well i hope u enjoy playing heimer as much as i do..Placing turrets is one of the most important things but you will learn that on time i guess..try to cluster em in triangles either defensively or offensive or in straight lines to hold a position...straight lines are awesome for mid iinner turrets the other team wont be able to go out and u will farm so much and get so much exp u ll be level 18 buying zonyas while the other team is still strugglign to buy some nice boots =) GL HF farm be rich and own.
MASTERIES: 9 on offensive... utility get the mana ones and cd other ones is your choice maybe gold clarity boost for team assist..u can even cooldown your summoner spell so your tele comes faster and clarity...Its really helpful but its up to you!!