I've often been the sole tester working for a startup, testing a web application and I loved it but it also required a lot of focus on what's important for a given release.
Learning to be a better tester is a very long, open-ended discussion but let me try to summarize some things that might help you now:
Your testing strategy (how you organize your testing) will be dictated by each release and the potential failures (or risk) for that release. Each is likely to be different. For one release you might focus on performance testing, another release you might focus on functionality testing or scenario testing, etc and yet another might be about bug fixes and so you'll focus on regression testing.
Good testing is about finding information. What is your information objective for your release? Talk to people about the release, what are we most worried about in this given release? Then search for information related to that objective.
Test documentation should be lean. It should help you to test but not become so difficult to maintain that it takes time away from testing.
Automation can help improve your efficiency. Not just with functional testing (regression testing) but also with creating test data, etc. Your programmers can definitely help you get comfortable with this.
In general when testing you can consider the following things:
- Coverage. How much of something has my testing covered?
- Activities. How did you test things? Did you use performance testing, regression testing, scenario testing, mobile testing, security, etc?
- Risks. Why are you testing, what failures are you looking for?
- Testers. Who does the testing? Subject Matter experts, beta users?
These 4 areas are important in helping you manage what you do and who does it. Since you are the sole tester knowing when someone else can help out, like a business person helping test certain features (as subject matter experts or as the person who requested the feature) might help free you to do more important or specific testing.
Testing is always about trade offs. We don't have time to test everything so which important things should we focus on in the time we have right now?
Focus on the higher risk items first and then lesser risked items afterwards.