I've never achieved anything great in LoL, just considering myself as a little above average player.
As I really like to play Nami because it's a very versatile support who can have use in any draft and situation and I really like to store and structure information for my own usage I decided to make an in-depth guide out of this. Hopefully it would help someone. I think this guide should be good enough for rating up to high-platinum/low-diamond.
Also excuse my terrible english.
W.I.P.
Any grammar/factology correction and suggestions are welcome in a polite form. As well as your questions! I'll try to response to everyone. But please, before you write a question make sure you've read the whole guide, answer might be somewhere in here already.

Now more details on summoner spells.

First of all Flash is a must have and I guess there is no doubt for that. Helps you to reposition in sticky situations or engage. Also serve as a source of escape.

And we're left with 3 options in our second summoner spell slot.

Exhaust is safer choice, scales the best among all three options. Take if you're inconfident, new to champion or position or enemy has assassin/diver. This might save your carry on laning phase, in teamfights as well as save YOU when getting focused.

Ignite is more risky, 99% of games you're going Summon Aery rune page with that. You have to play agressivle, poke, look for picks. Only time you're going this summoner spell with Guardian is when your lane opponent is a hard healer like Soraka as their heals might get out of hand quickly and result in lost trades/skirmishes.

Heal nothing special, always take this spell if your ADC decided to take something else instead of heal.

There is only two key runes to use as Nami support: Guardian and Summon Aery. Also I will have a word about Electrocute rune which is still pretty usable, but IMO it's only with very specific playstyle/situation.

Here I'll try to describe which options we're going with each key rune, why and how you should pick these runes.

Guardian

First of all, I want to point out that this rune seems to not be considered at all and everyone is just going Summon Aery. I can understand why high diamond+ rating player going that every game. They're confident in their laning phase and they will put a good use to this rune. But for lower ratings it's not the case. You should know what you're doing and your ADC should know what they're doing. Also in lower ratings games are longer and Guardian will outscale Summon Aery, especially because bigger shields are better and not only in late game. It scales with main stats that enchanter support items provide: bonus health and ability power. ALSO if there is possibility of split damage in early trades/skirmishes this rune comes in handy too.

Rune should be picked if you're inconfident in killablity of your lane or considering hard all-ins early game or very passive lane phase. As well as with weak and vulnerable early game ADCs, Vayne for example.

And I just like resolve tree. 90% of games when I pick Summon Aery I'm going resolve secondary as I like to have a little tankiness with Nami at all stages of the game.

FIRST ROW

For the first row the only option seems to be Font of Life. Works perfectly with your kit to pass on that rune in this row.

Although Demolish can put you far ahead in some situations, as every coin helps if you're playing support and might make a big difference in early game. It's not that high of a risk not to pick that rune, but I'm opting no to pick that in my games.

SECOND ROW

The second row here is just pure beauty.

Bone Plating helps you survive all-in and win short trades.

Second Wind is great against poke or high ranged line to help you stay healthy in case you eat couple of Caitlyn's AAs or Karma's Inner Flame randomly.

Conditioning is for passive line, once you're past 12 minute mark you will notice the difference with that choice.

THIRD ROW

As beautiful as second row.

Revitalize straight out buffs your shield and healing, even more in time of need (when your target is low health) and works perfectly with Locket of the Iron Solari and Moonstone Renewer. But even if you're building something else you can't go wrong with picking that rune.

Unflinching is kinda contradictory rune here. While helpful against hard CC lane opponent (if you're caught you're most likely dead, but coming out of CC earlier and cast one or two more abilities might turn situation). Then in mid game it fall off as if you're CCed you're 99.9% dead. But then in late game, if you picked tanky items, tenaciy is good again. So I'll opt into that rune if you have hard CC lane opponents.

Overgrowth just like Conditioning pure scaling rune. I'd suggest to pair this runes. The other two runes are obviously better at laning phase.

Let's wrap that up. If you decide you need, let's say, Bone Plating there is no reason to go Overgrowth, you better go with Revitalize which helps your surviveability as well or Unflinching if they have hard CC. Same applies with Second Wind, if you want more sustain early game Revitalize just works better. On the other hand you may take something except of Overgrowth if going Conditioning as tenacity scales with your tankiness (you're more likely to get out after CCed) and Revitalize is just a great rune.

SECONDARY RUNES

There is couple of options with that page.

INSPIRATION

Only two options here, but both are good for this rune page. Bacause we lack mana regen in very early game with this page I'd say it's almost mandatory to go inspiration.

Biscuit Delivery comes in handy as we're picking Relic Shield with that rune page and not going to have any other source of mana regen before first back.

Cosmic Insight literally every support mythic we use has cooldown on their active or passive which is reduced by this rune! On top of that you get summoner spell haste which is great because more uptime on summoner spells leaves you with more options and stacks up well with Ionian Boots of Lucidity.

DON'T FALL IN A TRAP PICKING Magical Footwear. At first it might sound good to get free boots with more movement speed as a support, but waiting for boots past 9-10 minutes mark might put you in very hidious situations. You need your boots earlier for rotating, warding, escaping, dodging, chasing and so on. Never take that. If Hextech Flashtraption seems just kinda useless, this rune might straight up ruin your early game.

SORCERY

This is more of a scaling/mobility rune page for us.

FIRST ROW

Nimbus Cloak is the best rune in its row. As we're taking Exhaust with Guardian page this rune will possibly save our live, as Exhaust has better range then Ignite it might help you to get out of bad situations and help to reposition yourself in fights too! With Ignite this rune also has an agrassive usage option. But if we pick this page we usually don't consider that option, so don't take it if you're forced to take Ignite on lane.

Manaflow Band is actually one of the worst runes in this tree while going sorcery secondary. When it's stack up (15 sec cooldown per stack) it gives you 250 mana pool and 1% mana regen per 5 seconds. Might sound good for sustain, BUT it doesn't give you anything when you need that regeneration the most. On laning phase. Procing stacks doesn't give you 25 mana, it just makes your manapool bigger. So 99% games we're not having any profit from that rune before 1st base. And for mid game we don't need that much mana regeneration, we're fine with what our items give. Also for example this rune regenerated only 862 mana for a 25 minute game where I stacked it up fast, because I was giga agressive at the lane and had several kills early game. This is why I would opt any other rune as sorcery secondary.

Nullifying Orb very rare occasion to go with this rune, but actually it might work against agressive double ap bot or supp/adc + jg (imagine Zyra+ Evelynn). Might save you a live. Pick this situationally.

SECOND ROW


Transcendence scaling rune. As we usually play passive with this page scaling is always a good option for a usefull stat. Ability Haste is always welcome and level 11 passive on this rune is absolutely nuts. In post 11 big fights this rune will shine.

Celerity good mobility rune. Pairs great with Nimbus Cloak and we pretty much always recieving movement speed buff from our passive which will be scaled too. Personally I would pick it only with Nimbus Cloak or Waterwalking.

Absolute Focus one of worst runes for secondary sorcery. Gathering Storm does almost the same and just better.

THIRD ROW

Gathering Storm just a good scaling rune. Good to pair it with Transcendence.

Waterwalking if you decided you want to rotate much early game this rune is good. Also good if you expect early skirmishes with midlaners and junglers involved as they happening on river usually. Also good for early dragons.

Scorch is a good rune, but don't pick it with that page. If we're in situation where we need to play it safe and can't poke we won't utilize this rune much and post 8-ish min it becomes worthless. Only for agressive laning.