How do I properly use Emiya?

I don't normally use him a lot though but his Hawkeye skill should be used with his Np to generate Stars and with his natural star weight, he will be the one to use them to perform critical hits unless he's not your main damage dealer so as much as possible; don't include a Rider that may steal stars from Emiya. This pairs well with the Additional Damage from Criticals on the same skill. It should be obvious as well that Projection is to be used on Brave Chains. That is how he is to be used with the recent update.
I have him at max lvl NP 2 but the lack of Buster Brave Chain from him spell utter failure from me. It is important to upgrade the skills since that will improve the damage.
For teams, I think you should be the one to think about that part. Not everything should be spoonfeed and it depends on the servants you have. Just use the ones you wanted to use aside from Riders since they will steal the stars generated from Hawkeye after you use your NP.

Basically with hawkeye he can generate a nice amount of crit stars with his np to then absorb and smack for hard hitting crits. In order to make him really shine you generally want someone to feed him extra crit stars like an assassin or maybe hans/other innocent monster skilled unit. Hawkeye is arguably one of the best crit amp skills in fgo and with archers naturally high crit weight it can be abused easily.

Skill level, team set up, Mystic Code usage, and your playstyle while using him.

Emiya is a Tough Crit Damager good for harder content, wave clearing, farming and boss slaying.
So many archer don't have good survival kit like Emiya ( Def up, Atk Down, Evade ).
With him you can dish out lots of damage while tanking damage as well.
He is also have one of the best Crit skill in the game Hawkeye along with 3 powerful all card steroid.

Like mentioned above, you need crit star gen supp like Hans, Crit damage + other damage steroid from Caesar, and Waver.

For example :
Emiya + Hans + Waver
Emiya + Hans + Caesar
Emiya + Waver + Caesar ( need Star Gen CEs )
Emiya + Fuuma/Jack/Cursed Arms + Hans
Emiya + Mashu/Asterios + Waver/Hans ( Stall Crit, Challenge Quest )
Emiya + OG Chu + Gilgamesh ( the most thing Emiya hates in the world )
Emiya + Proto Chu + Kid Gilgamesh ( he not really hate this for some reason )

For more advanced one, Emiya + Leonidas/Mashu ( Tank and die on demand/damage buff ) + Friends Waver ( 2030 recommended ) + Hans/other supps ( Come in after taunter/tank dies, buff ) + Caesar ( Atk, NP dmg, Crit dmg, star drop buff to Emiya ) + another Buff stacking servant/backup DPS/Last man standing ( anchor is more recommended, enough with the damage up +++ finish the enemy already ).
Switch and swaps for more simple combos.
Party comps can be changed based by the enemy or up to your taste.
Chaldea Combat Suit MC, has many uses for your Emiya and lots of team comps.

For more shorter fight/simple one turn kill, Anniversary Blonde is your choice while Chaldea Combat Suit offer more playstyle but harder to use ( seasoned and veterans top choice ).
Harsh and endurance battle, use Atlas MC.

That's only example, i don't know your supp or other servant in your Chaldea and at least that would be some little help for you.
Good luck trying another ways of using him.

Most of the times that you hear that a particular servant is good, you can assume that at least one or two of that servant's skills are a large part of the reason. That being the case, you usually need to level up those particular skills to truly utilize that servant to it's best potential.

In the case of Emiya, the reason that he's considered good now is because his 2nd skill gives him a 100% critical damage buff for 3 turns. This is very rare, as most skills with a 100% crit buff only last for 1 turn. 3 turn buffs usually only give 40-50% additional damage tops. In addition to this, Emiya is an archer, so he has a high natural star weight and will be able to get the majority of the stars that your team generates. Plus his 3rd skill can give him an additional damage boost for one turn.

So basically, the way to use him is to pair him with teammates that can both give him stars, and further boost his damage with additional attack and/or crit damage steroids. Then you pop his second skill and start critting the heck out of stuff. If you manage to get 3 cards in one turn, you can pop his 3rd skill as well, and wreck stuff even harder.

His second skill also boosts his critical star generation, so he can provide some of his own stars. However, his hit counts are low, and most of his cards are arts cards, so he will probably still need some external help generating stars. So you'd probably want to either run him alongside an assassin, or some servants that have passive star generation skills and/or fragment of 2030.

So an example team would be Emiya + Jack + Hans/Waver. Jack provides stars, then Hans or Waver will give Emiya both an attack buff and a crit damage buff, then Emiya pops his own buffs and goes ham on stuff. There are advantages to both Hans and Waver, so whichever you choose to use is up to your own preference. The advantages of Hans is that he actually can passively provide some additional stars to the team, and he can also increase your team's critical star drop rate, as well as provide some healing. Also, Hans' crit damage buff is team-wide, which is handy when you're running with Jack, since she will generally be getting some crits in as well. The disadvantage of using Hans is that you have to fire off his NP in order to provide some of his buffs, which means that you have to use one less damage dealing command card that turn. In addition to that, you will sometimes have to use his command cards in order to charge up his NP gauge, which means that you will be sacrificing some damage and stars on occasion, since you won't be using Emiya or Jack cards at that time. Also his attack and defense buffs can miss, albeit rarely. The advantages of using Waver is that everything he does is built into his skills, so you never need to touch his command cards. Plus he provides your team with an additional NP charge. The disadvantage is that he can't provide extra stars like Hans can.

Another example team is Emiya + Hans + Waver/Helena. But for this type of team to work, you'd need Fragment of 2030 on at least one of the supports, and ideally on both of them. This way, all of your stars are generated passively, so you don't have to use an Assassin's command cards. That means you can use more cards for straight up damage dealing, and for charging NP gauges. This type of team also has fewer RNG requirements, since the star generation is more predictable and consistent. Unfortunately, not everyone has the CEs required to make this work.

These are just two example teams. There are plenty of other options. Just find a way to feed Emiya stars, and he can wreck things.

Raising Hawkeye to lv 10 is quite important for his usage because that's his most important skill for damage and star gen.

People had already told you some strong comps to use him. As a general rule, anything that can feed him stars, crit up and overall offensive buff is good for Emiya. Merlin is also a powerful choice when he comes out, since he can buff his crit 100% more for one turn, strengthen Unlimited Blade Works and other benefits.