What kinds of things can I do to play Abathur better

Allmost all Abathur actions are related to map awareness. So keep an eye out where your "services" are needed. You mostly need to focus on the following:

• Send locusts in one lane, and use your symbiote in a different lane to spread your XP gathering. Locusts get XP from last hitting and give a little extra pressure to the lane. Your presence using a symbiote gives you the normal XP.
• If there are no allied heroes available to use symbiote on in a lane, use it on the healer of a minion group. This ensures you won't be focused down fast while still being close enough to gain the XP.
• You can use symbiote to increase the damage output of a hero, but you can also use it to shield and save heroes on the retreat.
• Having a more map based game focus gives you more insight in the state of the game. Try to predict what the enemy heroes are up to and make some calls for your team.
• Place toxic nest mines on strategic places where you think enemy heroes will try to hide (certain bushes) or have to run through: the bushes around the dragon knight shrines and the knight shrine itself.
• If you are sure an objective (tribute or knight shrine shrines for example) is free to take (your map awareness should give you this idea) use your deep tunnel ability to quickly grab it.

If you are very comfortable with your play, Abathur also makes for a great bait. However, make sure your allied heroes are ready to jump on the enemy hero that's trying to kill you.

Basically, you need to keep an open mind over the map. Find where the action is, and assist that spot. You definitely need to keep moving where you are helping out. You need to assist any skirmishes that break out over the field. If there are no skirmishes, then help someone take a merc camp or objective. Very rarely will you keep your focus at one spot. If nothing is happening around the map, then assist whoever might be taking an objective or pushing a base. As soon as there is action elsewhere, move your focus there.

TL;DR; Try to help the most intense spots at the time. If there is action at multiple places, you can choose to help out the place that is out numbered, or help the side that is outnumbered win there fight very quickly and then move to the outnumbered fight.