Having "the right" tools will not make you any better at writing, but they can make the process more enjoyable. Of course, the "right" tools are really what's right for you. I've found my favourite tools through a mixture of coming across them by chance (most physical products) and trying them out after reading recommendations by other people (most of the apps I use).
Here's the current suite of products I use for writing.
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I'm a big fan of the Leuchtturm 1917 notebook range. They're very similar to Moleskines, though the standard A6-ish size is a bit wider, and they come in a range of bright colours. I also like the paper in these much better than Moleskines, because it's thinner and smoother, and the lines are lighter—I find the lines printed in Moleskines are too dark, especially when writing with pencil.
Having said that, there's one exception for when I use a Moleskine. These cahier notebooks come in a pack of three and are the perfect size for a "workbook"-style notebook. I keep one of these on my desk all the time for writing notes, drafting outlines and exploring ideas. They go straight into the recycling after I move onto a new one.
I've tried many a pen over the past few years, and I'm quite fanatical about my favourites. I currently switch between just a couple that I really enjoy.
My true favourite is my Ti-Click Pro. It's one of the most refillable pens you can get, with a list of about 30 types of refills that fit it. Because of my love for extremely fine points, I tend to use refills that don't quite fit perfectly, but well enough. These days I rotate between a Hi-Tec-C Cavalier 0.3mm refill and a Uniball Signo 0.28mm. If I could find a fine-point refill in brown ink that fit this pen, I would probably never use anything else.
The other two pens I like to use are both included for one main reason: they come with brown ink. For some reason, brown ink really floats my boat, especially on the off-white pages of a Moleskine or Leuchtturm notebook. I use a Hi-Tec-C 0.3 or 0.4mm in sepia, and a Sakura Pigma Micron (although they're not really "writing" pens) 01 in sepia.
I use Brett Terpstra's Marked 2 for previewing Markdown files, checking links and copying the HTML version. One thing I really love about Marked 2 is that I can change the CSS to match my own site, and I can preview documents with the images.
When I'm editing a draft I use Alfred to access my Mac's built-in dictionary constantly. I rely on this every day to check spelling (especially US vs. UK versions) and definitions.
For editing images I use Pixelmator for all the heavy lifting, Skitch on occasion for adding arrows to point things out, and Status Magic to remove all the unnecessary junk in my status bar for iPhone screenshots.
My research happens constantly, whether I'm working on a piece or not. It's a continual process of reading, collecting and filing away anything that could be useful to me. I use Pinboard to save links for research and add two or three tags to every link so it's easy to find again later.
Update: I now use my own tool, Larder, instead of Pinboard.
Although these tools make my workflow faster and easier right now, I've realised that there's freedom in switching tools when I have a different need. If I'm working on a different type of writing or I've discovered a better way to save my research links, I'll switch to tools that enable that process instead.
Start with your process and look for tools that fit.