Perhaps the most important thing the internet has done for us is to make research so readily available. I was an English major in college and avoided library research as much as I possibly could. How? By using interent resources. Now, you have to know how to negotiate the credible sources from the bullshit ones, but, in the case of simple fiction writers like us, a quick wikipedia search can make our lives way easier. For example, I was trying to flesh out one of my stories with a suble allusion to the vampire myth, but wanted my details to be as realistic as possible; I wanted to go further than Bram Stoker. What I found, with a quick and simple search, was information on Elizabeth Bathory, a Hungarian countess from the early 15th century who is reported to have tortured hundreds of girls and drank their blood because she believed she could stay young forever this way. Bam! This turned out to be the detail I needed (and also perhaps some of the very same source material Stoker used for his own ideas). I keep an internet browser open and ready to go when I'm writing; you never know when you might need a reminder about something, or a bit of history, or name idea, etc. Also, if you haven't already, I'd highly recommend getting a smart phone; having Google there in your pocket to look things up whenever they spring to mind is absolutely brilliant!
The internet is also great for the technical stuff. I can't imagine how difficult it must have been for reporters to get their quotations right before digital recording; I also can't imagine having to find the exact place in the book of the famous person you're trying to quote correctly. It is very easy to find excellent quotes from all kinds of public figures with a quick online search. Besides quotations, you can also easily find information on how to cite your sources correctly (If you've ever writen an academic article you'll know there are several ways to do this and the rules are complex - MLA, APA, Chicago, etc.) and how to format your manuscript. When I finish a story, the first thing I do is put it into standard manuscript format. You'll still have to very carefully read over each publication's specific formatting guidelines and make a few tweeks before submitting your work, but it helps to have a starting point.
Which leads us to getting published. The Internet has made the submission process WAY easier! There are still publications that require the traditional submission method -print on this kind of paper, mail this special way, wait 6 months and you might get a reply, blah, blah, blah - but most publishers, at least in the Speculative market, accept email or electronic form submissions. I have submitted work both ways and, let me tell you, I much prefer to submit electronically. It is also much easier to find places to submit to on the internet then picking up one of those 'Writer's Market' books and leafing through all the places that may or may not be still in business or accepting submissions or even looking for the kind of stuff you write. Electronic submissions has made the world a much kinder place for both us writers and publishers alike.
Did I mention smart phones yet? A lot of the mobile devices out there can be a great asset for the 'writer-on-the-go.' For starters (and this is huge!), start saving your work on some kind of a server program. I'd recommend Google Docs, or you can use DropBox, or Mobile Me, or whatever. Save your work in the "Cloud." At least back-up your work this way. I have my entire life's work of writing, notes, text conversations, and everything saved into Google Docs; that way, if my computer crashes, and my house burns down, and my work computer blows up, and my phone falls in the duck pond, and all of my printed manuscripts spontaneously combust - all in the same day - I still haven't lost any of my work. All I have to do is sit down at any ol' computer and pull up my documents. I know, some of you might be a little wary (especially those of an, shall we say, 'older' generation), of putting your work into such a system, but believe me, it's all very secure. Worst case scenario: someone does manage to hack into your account and somehow publish something of yours under their name - well, you own the rights to your own writing as soon as you write it and now you get to sue the pants off someone! Hell, you'll probably make a lot more money suing someone for plagiarism then you would for actually publishing it yourself! Anyway, saving your work in the 'cloud' can make it really easy to open it anywhere so you can bang out a couple hundred words at lunch or whenever.
Try using an app like 'My Writing Nook' on your smart phone to pull up your work and get a little writing done while riding the bus or in the waiting room at the dentist's office. I've done it. Besides, we don't all have these huge chunks of time to sit down at our desks at home and type away. If you really have the drive to write, you'll find the time to write no matter what. I write during my lunch breaks or during slow periods at work. You might find that a lot of your best writing is done in quick, passionate spurts anyway. A lot of us dream of being locked up in a big, quiet mansion somewhere for several months without responsibilities or interruptions so we can write the 'Great American Novel'; the real world just doesn't allow us (most times) to do this sort of thing. Remember what happened in "The Shining," the supposed "perfect" situation for the aspiring writer; Jack Torrance sure didn't get much writing done, did he?
Anyway, here are a few links you might find helpful:
Writing.com — It can be really helpful to be a part of an online writing community. Some useful tools and excercises.
Style Guide — Every writer is going to need this thing at some point. An excellent and easy to use reference for when you have style questions.
www.mywritingnook.com/ — This is that App I was talking about earlier that allows you to save your writing and access it from any computer and any mobile device. I use it to write on the go.
docs.google.com/ — Google Docs! Save all your work on this site and access it anywhere. Yay!
www.writing-world.com/basics/manuscript.shtml — This page will give you all the basics when it comes to proper manuscript format.
Seventh Sanctum — Do you have a difficult time naming your characters? Check this site out. I think it's especially useful for writers of fantasy, but it offers a variety of name generators for people, things, places, organizations, etc.
AutoCrit Editing Wizard — This program searches for overused words, repeat phrases, and sentence length variation. Anything greater than 800 words and you'll have to pay, but it is pretty helpful.
Web-Chops — If you do a lot of research online, this tool might help. It lets you collect information from different places around the web and place it in one place. I haven't used it too much, but so far it seems pretty useful.