Nova is notorious for picking off players while roaming around to get her team ahead. This is particularly strong because of the objective control that she gives her team. Because Nova is permanently stealthed, this means she can roam around relatively safely, even if she encounters a group of enemy heroes taking a camp or handing in an objective. The downside to doing this as Nova is that sometimes (particularly in solo queue), you get blown up. Hard. We can mitigate this by taking Abathur, and having him symbiote onto us for most of the game. This is particularly strong because while Nova already does incredible burst damage, when you add in Abathur's contribution, she can easily 1v1 a Valla who is 2-3 levels ahead, or even 2v1 most heroes if they are on the same level or lower than her.
Overall, you do not take Abanova to just sit in lane.

YOU ROAM AND PREVENT THE ENEMY TEAM FROM GETTING OBJECTIVES.

You should be riding between lanes, picking off squishies and anyone who might be low, as well as poking at heroes and just generally giving each lane an advantage. I cannot emphasize enough that you should not be staying in lane for any reason except to save a fort/keep.
On Sky Temple, when you notice that the enemy team has taken a temple, hide outside the temple and distract them with clones until one of them is low enough from fighting at temple for you to pick off, and then scare away the rest. Your team should help you out if there are more than two.
On Dragon Shire, roaming between top and bottom lanes has never been more effective. When the shrines turn on, be ready to head to whichever one is in a solo lane, and co-operate with your laner to blow them up when they inevitably go to try and contest the shrine. You can then roam to the other shrine to help keep them off that one.
Spider Queen plays out pretty much the same way as Dragon Shire for this, just roam between the two altars and gank lanes when needed. Try to keep an eye on all of the enemy laners to see when they are going to pass in, and then contest them. If you don't feel confident taking them down, use your clones to harass and keep them from handing them in until backup arrives, or until you poke them down enough.
Blackheart's Bay is great for this comp. Way too often in solo/duo queue, I find people just walking up to Blackheart alone, and since you're really two people, you have the big advantage, and you'll be able to blow up anyone except maybe Illidan.
Cursed Hollow is a bit harder for Abanova, but it still works. Try to communicate constantly with your team (you should be anyway!). Make sure that when tribute spawns, your team is either ready to push their lanes all the way in, or ready to contest the tribute. Since you can use clones to draw people off of tribute, you should try to stall them any length of time you can, even if your team is planning on just pushing the lanes in instead. It maximizes your EXP soak. Don't underestimate the amount of damage you can put out at level 7.

As your vision will largely be focused on Nova, who is not dedicated to a single area of the map, it is too risky to attach your Symbiote off of spawn pad. Because of this, your locusts will see little if any use, making locust traits redundant. Likewise, for this role, you will have little if any chances to reliably place Toxic Nest, though on most maps you can still move out to place them while still being in the safety of your keep or fort. Instead of these abilities, you instead focus on the abilities you acquire on your symbiote. Early game, the regeneration from Regenerative Microbes makes the difference between being able to pressure once and being able to pressure multiple times before having to return to fountain or base. Additionally, if you and your Nova have recently punished an enemy lane and your ally laner is low on health, it is usually well worth the few seconds to switch to them to apply one or two rotations of healing. On early game heroes with potential sustain such as Arthas, Valla, or Sonya, a single Carapace in combination with their in-kit regeneration is often enough to substitute a fountain run.
Since Nova is responsible for much of your movement and fight picking capacity, your use will be more standardized across the maps.
When Nova is wandering between lanes or objectives, she may be vulnerable to being ambushed. Your shield and heal are often sufficient to allow her to survive trades with single heroes, and your Spike Burst will lay heavy damage on any heroes that stay within close range. A useful utility to avoid walking into a dark area is to scout with your Stab, the shot has a decent range on it, especially once upgraded, can pass through walls, and it makes a distinct sound when it hits a target. Assuming your games are not muted, both you and the Nova can hear this, and it is warning enough if there is someone in the bushes or around the corner. While Sustained Carapace is a decent choice for the extension of heals, Adrenal Overload is a considerable boon to Nova, as it synergizes with her kit to partially mitigate the Attack Speed loss from her Anti-Armor Shells, and it is generally more beneficial early game if you attach to other non-Supports.
Many Abathur players will take the Spatial Efficiency trait religiously, but as a damage output, it is on a low enough cooldown that the third stack is unnecessary. Besides, your damage is merely a bonus, the point of Novathur is to use Abathur to help keep Nova alive. By that extension, Soma Transference makes for a major failsafe should Nova or your current host be jumped on, and it can stall long enough for the Carapace heal to take effect.
Because your biggest asset as Novathur is your map presence, it is vital that you can get Nova, as well as any other key heroes where they need to be quickly, be that to take an objective, to pursue an enemy, or to flee to fight another day. The speed buff from Adrenaline Boost is simply too overall useful to give up. In addition to the shield and heal, it can be used for almost any scenario.
Your choice of Heroic Ability depends very greatly on what your team needs of you. On most maps, if your team has adequate control of Objectives but is struggling in Team Fights, you should take Ultimate Evolution. Having two(and up to six!) Novas can be something of a nightmare to an enemy team, especially if they all focus the same target. There are few heroes that do not benefit a teamfight by having a double. Tanks and Initiator doubles, such as Anub'arak or Sonya allow for further lockdown on the front line, and a duplicated support such as Li Li or Malfurion allow for an often underestimated staying power in your team as a whole.
However, if your team is dropping like flies, or the map objective depends on Minion Equilibrium such as Cursed Hollow, Evolve Monstrosity can save games. Attaching your Symbiote to the Monstrosity allows you to control it, granting you the closest thing to a genuine combat Abathur. The Monstrosity can compensate for lack of minions, and with the boosts the Symbiote will provide, the Monstrosity will survive until either you attempt to solo a fort or keep, or they send an enemy hero to take it out(heroes that are behind or have low DPS may actually get killed by the Monstrosity instead!). Because of its considerable attack damage coupled with Adrenal Overload, it may also be used to speed up the clearing time of Golem(Haunted Mines), Webweavers(Tomb of the Spider Queen), or Shambler(Garden of Terror).
If you have chosen Evolve Monstrosity, you may choose to take Evolution Complete to allow it further pushing power, allowing it to tunnel to any location you have vision of. Otherwise, your most useful level 20 trait is Hivemind, which allows you to have a secondary Symbiote attached to a nearby ally. This allows you to launch a second cast of all of your Symbiote abilities towards your desired target, effectively doubling your damage output, and allowing you to stack your healing shields, which can turn teamfights in the late game.