How do I estimate how long it will take me to ride my commute? How can a cyclist, new to commuting by bike and not all that experienced in riding, estimate how long a commute will take?

I have been riding for 4 days to and from work. 156km over over 4 days. I'd like to know what I should be averaging time wise. I am 203 lbs / 92kg, and somewhat fit. The ride is 13 miles/ 21km there and back with an elevation of 81 meters and I'm using a good standard bike. 

Are there any general guidelines to use to get an estimate? What factors will affect this? (Fitness, traffic, etc.) How can I identify ways to get faster? (Routing, accounting for other delays, etc.)
Unfortunately, there is no single answer to this question. In my experience, every route is unique, and will have variables that increase or decrease the transit time for a particular commute.

Traffic, seasonal weather, time of day for the commute, rider's fitness, and your bicycle's condition will all play a role in determining the time for a given route.

If you are regular cyclist, and have an idea what your average speed is on a fitness ride, using that as a basis to gauge how long a route will take is a good start.

When I ride a route for the first time, I gauge the time by average speed, and then if there is a deadline for me to be at the destination (i.e. I have to be there and ready for work at 9 a.m.) I take my fitness time, and double it. That ensures that I have enough time to arrive, even with problems I don't foresee. Then I add 15-20 minutes, to allow myself time to clean up and be presentable for work.

The next step is to ride the route. If you are especially cautious, then informing your coworkers/employer that you are trying a new route to work and might be late, if you have unforeseen issues, is not a bad idea. Doing a test ride when you don't have a critical deadline, meeting, or even doing it the first time on your day off, is even better.

You will get used to traffic patterns, weather issues, and normal delays. Even once you are certain of the normal time a route will take, it is a good idea to allow a bit of leeway for a flat tire, or an unforeseen circumstance.

I know that the answer you want is something along the line of x kilometers or miles will take y minutes, but that is not possible to gauge for you. What we can offer, is ways to learn the time for your route, without causing damage to your life or your job.

I hope that is helpful.