In this guide...
If you want to learn about how Nami can really shut down mid lane, welcome!
If you want a prettily formatted guide, please check out many of the other guides.
Please refrain judgement unless you've actually tried this out. It's alarming how powerful Nami is when played as a mid. Simply alarming.
I guarantee that the majority of those who have down rated this guide have done so without any experience testing this build.
I'm not sure when I will add more to this guide, as I am currently doing it out of boredom, but I'll try to add more to it soon.
Riot says she's a support/She scales so bad/She can't carry/Nami go bot/etc
Nami is quite possibly the dirtiest counter character you could imagine. Riot gave a character an ability which simultaneously harasses for respectable skill damage and then heals for an equally respectable amount. ABUSE IT.
Nami can shut down any mid (although it is harder to shut down morganna, fizz, and the rare ap yi due to blackshield, troll pole, and alpha strike respectively--possibly others like morde). If her W scaled well, she would be an immensely broken carry... but scaling well doesn't mean anything in the first third of the game, giving Nami an immense lead. Using W over and over one of the following things is guaranteed to happen:
1) You will kill your opponent.
2) You will force your opponent back over and over while you stay in lane free-farming.
3) Your opponent will have someone from another lane come and lane with them as your harass is too much to deal with alone.
Important notes: Most people can't see the potential of Nami's solo capabilites if they've played her as a support because honestly, her W functions very wonkily with an ally and two enemies--in these conditions, it's unreliable. In a 1v1 setting, it's extremely reliable. You will harass them for free or you will get healed and when the trade for harass.
Extremely Important do not try to play Nami as an AP mid. If you do, you will be outscaled. You must build Nami as an AD carry if you play her mid, or you will be forced into the roll of support later. Nami will still be a capable support who shut down their mid for the first third of the game, but an AP Nami will ultimately not do enough damage to carry a team.
So what do I do?
Get W first, help your jungler get blue or red, then go to lane and harass with W whenever you have the opportunity and are safe. Farm by last hitting creeps with auto attack. Do not waste your mana or safety by expending a Q or E to farm.
Important: be very careful of a mid with a stun, flash, and especially ignite at levels 1-2 because if they surprise you you may end up trading or potentially dying yourself if things go extremely wrong.
By level 3 you'll have 2 ranks in W, and you will be severely outclassing the opponent. Every single exchange you will W them and run, W them and run, W them and run until they're extremely low on life.
Keep in mind the opponent will eventually realize (if they're intelligent) that at Nami's W's max range they can run away and take the damage but run away too far for the bounce to reach Nami. This means Nami will harass but not be healed. The opponent will have to choose between hitting Nami and accomplishing nothing, or running from Nami as they try to farm. Either way they will lose this trade. If they ignite you early to try and prevent you from healing, Q on yourself and slightly towards them to run away safely (with faster movement speed from your passive and from them being stunned by your Q).
Next the jungler WILL gank you. They have to. You are completely dominating their mid.
To get the most bang for your buck:
Nami's E is very interesting in that it can be activated while a projectile is already in flight and will apply it's effect on that already-shot projectile. In other words, if you shoot, then E yourself before that shot hits the person, they'll get slowed. With that in mind, this is how you should always use your E, in mid shot.
If you're hurt and your opponent has figured out they can run away from your W to prevent you healing while you're harassing them, you can start the harass by healing yourself. This guarantees you'll get your heal and your harass, but try to only use this once they've caught on as it may alter how they play.
When chasing someone, don't be afraid to E whoever is closest to the target so that they can slow the enemy. Try to only ult after someone is slowed, as Nami's ult isn't particularly hard to dodge if it's coming from a long distance.
Whenever your opponent is extremely low on life from your non-stop harassment, the ideal, though not always practical, skill sequence to kill them is: auto-attack (E to slow) followed by Q, auto-attack (refreshing slow) followed by W, followed by your third auto-attack or ultimate to finish them off. It is very hard for them to escape Nami's ultimate when they are slowed by her E and trying to run for their lives. Odds are, the wave will kill them.
There are a lot of options open to Nami when ganking, so I'll skip the fairly obvious ones and go into more interesting ones.
Nami's ult hits a huge area. If you're ganking someone bot or top with flash, Ult at the wall cutting off the direction they will run by how far they'll run + a little bit more (for flash) and the enemy you're ganking will have 1 of 2 options: 1) They are forced to stop and let the ult pass, as your teammates and you pick them apart. 2) They try to flash over the ult and get caught.
Bush + slow:
If you're ganking for bot, or a ranged top, you can have that teammate push forward so that sight is cut off from one of the bushes. Just like a jungler might, you sneak in, but this is where the similarities end. Instead of waiting for the lane to get pushed back, all you need to do is have your ranged teammate harass your target one time. Wait for them to start shooting, then E your teammate to apply the slow. Immediately ult the obvious path they'll take and walk up to finish the easy but very impressive gank.
If you are not extremely comfortable with this build, do NOT mid against a Fizz. The matchup is incredibly difficult. He's very hard to shut down and if he is able to actually get to you, you will probably lose in the trade (which defeats the entire purpose of this build). I strongly recommend that you do not play against a Fizz mid.
Morgana is harder to force out of lane or kill than most mid champions because she can heal up on minions and time her black shield to prevent you from harassing her. This is very mana intensive, however, and requires her to push her lane forward to your tower, making her fairly unsafe if and when she's unable to blackshield (or if your jungler stops her early.) After a single death in which you stay and farm (for the exp mostly in this case) Morgana will have extreme difficulty keeping herself safe.
Morde, like Morgana, has to push his lane to save himself from your harass.
This matchup is very tricky if the Yi player is careful. Ultimately AP yi pushes the lane forward just like Morgana, however he does not really care about your harass because of his meditate. You have to save your Q for when he meditates to stop him from gaining the life but be wary about doing this if Yi is in a good defensive position as Q is your primary escape tool, and you could get ganked while Q'ing Yi.