To do a good job you want to focus and pay attention. You want to be hard-working and persevering. Below are some words that mean to word diligently and persistently at a task.
Imagine studying GRE vocabulary (this shouldn’t be too tough!) via flashcards. You take them out of your pocket every now and then but otherwise you approach is pretty haphazard. Contrast that with an approach in which you carefully make sure that you keep track of each word you miss, creating a separate pile for such words. Later, when you get home, you write down the words that you missed, and put them on notecards, which you plaster throughout your house. The latter is an example of a sedulous approach to studying GRE vocab, one that shows dedication and diligence.
It’s easy to give up — whatever the task may be. To keep at it diligently is to be assiduous. Assiduous implies great care. So you may continue doing something, but lose heart. In that case, you’re not being assiduous.
To learn a new language you have to be assiduous, seeking out native speakers, drilling grammar, and listening to tapes whenever you have a free moment.
Another word denoting hard work, industrious, doesn’t have as much nuance as assiduous and sedulous. I picture an office worker, head down, trying to get his or her job done before sunset. Sure, he or she is probably being careful, but industrious is more about being focused and hard-at-work. An industrious student of the GRE will work hard. But I’d put my money on the sedulous one, who is not only diligent but also exacting in how he or she gets the job done.
With alacrity we move away from hard work and focus more on a willingness to do something. A new hire is likely to work with alacrity, hoping to impress the boss. If you enjoy camping, and your friends invite you camping, you are likely to do so with cheerful willingness or alacrity. In both cases, you’ll likely do a good job, whether finishing a project in record time or pitching your tent against a rock. The adjective form alacritous is not as common, but if you are serious about learning vocabulary, you’ll memorize it with alacrity.
Sometimes, being very careful and diligent is not a good thing. Somebody who is punctilious overdoes being detail-oriented and hard-working to the point that it comes across as annoying. Imagine a waiter hovering over your table throughout dinner, making sure you knife and fork are always parallel, and filling your water glass every time you take a sip. He is acting punctiliously.