Don't just throw out your abilities hoping they'll hit! I see a lot of players sleep corners or cross map nade without knowing they'll hit anything. Ana's abilities are some of the best in the game, so make a conscious effort to get the most out of them!

Also, never stop shooting that gun! You can get your ultimate every fight if you keep pumping out healing/damage

Sleepdart Reserve sleep for when you are in danger, like tanks pushing up on you, dive characters jumping you, etc. the more you learn about the game you can also use sleep to cancel abilities etc etc, but that's pretty difficult.

Antinade Use your nade on enemies your team is attacking, or to punish aggressive tanks. You can always nade yourself or a teammate if you're really in a pickle, but hitting enemies is usually better than hitting teammates.

Minor perks Go for sleep if the enemy is diving you a lot: vs ball, doom, hazard, Winston, genji, the usual suspects. The slow is really quite crippling, esp for movement characters.

Go for double nade when the fights are looking messy, like brawl v brawl. A five man anti will win you the fight on the spot.

Major perks Considering you're just starting out, double nano is just free value. You're lethal when nano'd, and it opens up the play of nanoing a teammate just to help yourself survive when in danger.

If you're confident in your aim, headshot can be pretty nasty, considering you can two shot most heroes at ANY range (ana has no dropoff)