Hello, everyone!
Nami is my favorite champion, and she is my main.I hope you get to know her better with this guide :)
Nami is an easy and fun champion to play, but she can cause a really big trouble for the enemy team with her strong crowd control and long distance ultimate.Also, she is a great harasser and very annoying sometimes.

I am the tide, and I cannot be turned. - Nami

Pros;

+Great harasser
+Good crowdcontrol with her Q and W
+Long distance ultimate, engage/disengage skills
+Fun to play
+She is a mermaid

Cons;

-Squishy
-Easy to play, but hard to master

At laning phase, you need to take care of the AD carry.Your job is to make sure your carry won't get killed in seconds.
As a support, you need to support the team to get kills to be successful.It might be hard if you main the other role because you need to bait and get them to pay attention to you.Being a support is more than just standing and feeding the enemy.Supports are important!A team without a support probably not a successful team.

Personal experiences

People (especially in bronze and silver) think being a support is boring and awful.It makes me angry when someone says 'I don't play support' or when I play as an AD carry someone brings Riven as support.This way you can't be supportive (but there are always a few exceptions).

When Nami's abilities hit allied champions they gain Movement Speed for a short duration.
Sends a bubble to target area, dealing 75/130/185/240/295 (+50% Ability Power) magic damage to enemies, and stunning them for 1.5 seconds.
Unleashes a stream of water that bounces back and forth between allied and enemy champions.

On Ally Hit: Heals 65/95/125/155/185 (+30% Ability Power) Health and will bounce to a nearby enemy champion.

On Enemy Hit: Deals 70/110/150/190/230 (+50% Ability Power) magic damage and bounces to a nearby allied champion.Bounces to each target only once, and hits up to 3 targets. The damage and healing value is modified by -15% + (7.5% per 100 Ability Power) each bounce.
Empowers an allied champion's next 3 basic attacks, causing them to slow the target by 15/20/25/30/35% (+[5% Ability Power]%) for 1 second and deal 25/40/55/70/85 (+20% Ability Power) bonus magic damage. Lasts for 6 seconds.
Summons a Tidal Wave from Nami's position. The wave knocks up enemies and slows them by 50/60/70%, dealing 150/250/350 (+60% Ability Power) magic damage. The duration of the slow increases based on how far the Tidal Wave has traveled, with a minimum duration of 2 seconds and a maximum of 4 seconds.Allies hit by the wave gain double the effect of Surging Tides.

The risky way

I start with Aqua Prison because if the enemy is trying to kill me or the ADC in lvl 1, I can stun them and we can escape.Also if they invade it is better than W.
Next Ebb and Flow because this skill allows you to heal and damage at the same time.
At lvl 3 Tidecaller's Blessing.
After this, I start maxing Ebb and Flow because it is Nami's most used and needed ability.

The safer way

For a more safer start, you can start with Ebb and Flow.
At lvl 2 Aqua Prison is needed because for example if you play against Leona, you can escape with your Q.

In both ways you should max W.

Since the mid season update came out, support items changed a bit.I like how did they changed because this way supports are not 1 or 2 levels behind and can actually earn gold and exp.Since Spellthief's is the most common starting item for Nami, you can use her autos to poke the enemy and you will get gold for it like before.But now, if you kill a minion, this passive disables for 6 seconds.So the quest is to earn 650 gold with Spellthief's passive.After you finished the gold collecting, Tribute will be upgraded to Queens Tribute, causing procs to grant a short burst of movement speed.

Ardent Censer: Gives +10% bonus healing and shielding power. Heals and shields on allied champions (excluding yourself) enhance their basic attacks for 6 seconds. Granting them +20% - 35% (based on level) attack speed and 20 - 35 (based on level) bonus on-hit magic damage healing them for the same amount.

Rylai's Crystal Screpter: Damaging abilities and pet attacks slow affected units by 20% for 1 second.

Athene's Unholy Grail: Gain 25% of the premitigation damage dealt to champions as Blood Charges, up to 100 - 250 (based on level). Healing or shielding another ally consumes charges to heal them, up to the original effect amount.

Mikael's Crucible: Gives you the ability to use cleanse which can be really helpful if the other team has more cc.

Zeke's Convergence: Casting your ultimate near your ally summons a local frost storm for 10 seconds. As the storm rages, nearby enemies are slowed by 20% and your ally's attacks burn their targets for 50% bonus magic damage over 2 seconds (45-second cooldown).

Banshees Veil: Grants a spell shield that blocks the next enemy ability.Gives magic penetration too.

Banner of command: Gives armor + magic resistance.Also, you can promote a minion.

Frozen-heart: Buy Frozen Hearth when you have a heavy AD carry in the other team.

Sorcerers Shoes: Gives 15% magic penetration.

Boots of Swiftness: I often buy this when Jhin is the enemy ADC or midlaner because of his traps and ultimate.

The Japanese word 'nami' (波) means wave.It's written with the same kanji as 'tsunami' (津波).

What should you do?

Laning Phase

Your main job is to protect and keep alive the AD carry.
Always ward the river, especially when your carry is immobile (like Ashe) and easy to kill when the enemy jungler is ganking.
Look for opportunities when your W can jump to as many champs as possible (max 3).
Try to heal your AD carry when Ebb and Flow can reach the enemy.
Keep the distance but poke them with your Q and W and Auto Attack.
Always keep moving!This way you can dodge the stuns and your wrist stays warmed up.
Say 'gj' 'nice' 'wp' to your ADC (or teammates) when he/she gets kills, or destroys the first turret.He/she/they will be happy to hear that and he/she/they will might be less nervous :)

Team Fights

Don't run into the crowd because Nami is paper and keep the distance! While you areable to heal your team.
Use Tidal Wave to engage or disengage a fight (like poppy's ultimate).Your ultimate gives movement speed so your team can escape or attack back.
You can be game changing so be ready to use your Q, W and ultimate.Drop Redemption and use Solari when the right moment comes!
Try to catch as many enemy with Q as many you can.

Nami channels the primal energies of the ocean, harnessing its mystical restorative properties and commanding the raw power of the tides themselves. Though many doubted her, Nami had the bravery and determination to take on a dangerous quest when no one else would. Now her people believe she is the Tidecaller, a chosen one destined to complete a quest essential to the survival of her entire race.

The Tidecaller's sacred duty is to acquire a moonstone, a powerful object found only in the towering reaches of the surface world. Her people, the Marai, rely on the moonstone's light to ward off the terrors of the depths. However, the stone's power lasts only one hundred years. Before its light fades, the Tidecaller must journey into the Great Deep, retrieve an abyssal pearl, and carry it to the surface. There, on the night of the winter solstice of the hundredth year, the Tidecaller makes a ceremonial exchange with a landwalker bearing a moonstone. By trading the pearl for the moonstone, the Tidecaller ensures the survival of the Marai for another century.

However, in Nami's time, as the hundred years drew to a close, no Tidecaller had been found. Without a chosen one to complete the quest, her people would face disaster, but the Marai waited in faith that the Tidecaller would appear. Nami refused to sit idle, insisting that without a Tidecaller to save them, someone had to act. Bravely, she decided to begin the quest herself and ventured alone into the dangerous depths. None expected her to survive, but after six days of battles with untold horrors, Nami returned with the pearl in hand. The Marai hailed her as the new Tidecaller. All that remained was for Nami to journey to the surface and complete the exchange.

When Nami arrived at the surface, however, she found only an empty shore. She waited for days in a mystic cove, unsure of what to do. In all the legends of the Tidecallers, the bearer of the moonstone had never failed to arrive. Nami faced a choice. She knew the surface world only through tale and rumor, but the survival of the Marai depended upon her. Summoning the tide to bear her ashore, Nami began her search for the moonstone and became the first of her kind to explore the world above the ocean. She left her home behind and vowed not to return until she had completed the Tidecaller's quest.