Naafiri is a scaling champion. Don't play for lane, play for game. Your most important goals will be staying up in farm and being ready to grab any opportunities. You want to be up in items for any skirmishes and teamfights, so always keep farm and staying alive at higher priority than trading kills.
Your dogs provide both a unique defensive tool as well as unique utility, make use of this :)

In lane. You want to play similar to a mage. You try to keep your distance from your enemies and poke with your q. Try to hit both minions and your enemy laner with at least one q, in order to both secure farm and keep up your sustain with taste of blood. If you manage to land both q's you also get your innate Q healing, which is very very beneficial.

While doing this, try to keep your pets alive as much as you can. They help with last hitting and give you extra damage and safety. They block skillshots for you, provide an extra delayed hit after your basic attacks and will nearby minions for you once every 10 seconds while idling.
To do this, make sure to cancel their aggro often. After you land a q, autoattack a minion. Whenever you hit a target with an attack or ability, your pets will immediately dash to them, so if you use your q on your target, they will dash to them and the auto afterwards has them then dash to your target minion, keeping them safe from harm. If they do not dash or are low on health, you want to use your e away from your enemy laner, to teleport your pets to you and reset them to full hp.

To summarize, keep your pets alive and poke your laner through the wave as much as possible.

As a laner, you will get ganks every now and then. To counter this, ward of course. The problem is, as naafiri you will likely be pushed into your enemy laner a majority of the time attracting ganks more often. To avoid this, don't immediately run away when you see an enemy. Your first response when you get ganked should be to try to double q the nearest enemy champion, they will most likely be tunnelvisioned on you and forfeit dodging it, giving you a free heal and phase rush activation, letting you get out with ease.

Midgame starts once you get to two items. In the midgame, your priorities are staying farmed up and keeping an eye on the map for fights. You want to be present at as many fights as you can and try to be present before they start. Whenever an objective is about to spawn, you want to look out for any enemies getting separated from their team and you want to take them out before the objective even spawns. You will mainly be sidelaning, but you will switch between lanes often in order to make it so enemies won't expect where you are.
You will
1. check the map for the next objective spawn + allied positions
2. walk into a lane
3. push it out asap
4. walk into nearby jungle and clear vision
5. hover there and keep an eye on the map for any isolated enemies (an unattended enemy botlane duo counts as one isolated enemy)
6. if an enemy overextends, head over there asap, pop ult and try to kill them safely.

repeat of midgame, stay in sidelane and hover for objectives but play more with your team. Try to take out threats before they become a threat to your team. In teamfights, you excel both in front to back fights and straight up diving so plan out which route you wish to take before a teamfight. Most often you will start a teamfight front to back, playing more as a mage and poking the enemy frontline down. Once an opportunity arises where an enemy squishy steps up too far, you want to take that opportunity to get on top of them instantly. Unlike other assassins, you do not need to stay out of sight as much at the start of a fight, because you are capable of fighting front to back too.

Of course this is simply a general guide, every situation will differ and as you go, you will find that different situations require a slightly different approach, but naafiri has the tools to tackle any of these situations. Play the dog plenty and you will get used to them. She is more than just a simple assassin, being able to fulfill a plethora of roles and having unique synergies both with several items, runes and champions.

And finally if you do get into her more and want to get a skin, make sure to buy your RP for cheap on lolrpshop.com and use code DAWG for 5% off :)