Once you've passed through the quick sign up process, it'll take just about as much time to learn how to use the web app. Bunker App walks you through the process of creating projects, clients, and invoice with handy, unobtrusive tool tips. It's not too different than most task management apps, in that you create a task under a project header and assign a due date (if desired). You mark tasks a done when you've finished, and that's that. When you're ready to bill a client, you just choose one of your projects and generate a new invoice. After filling out a little information, you'll have a linkable invoice like this sample I made.
As for downsides, you can only have two projects (and therefore, two invoices) for free. If you want unlimited everything, it'll cost you $US5 a month (which seems pretty reasonable). Bunker App is also pretty minimal when it comes to features, which may be good or bad depending on what you're looking for. If you're just getting started with freelancing, however, it's a simple system you won't have to learn.