You don't require any special equipment for a french seam, but I heavily recommend you have two kinds of fabric markers: One that will iron off, and one that won't. This is because we will want to clearly mark both seamlines in advance, and in between stitching your seams, you will be ironing and you don't want your second seamline to iron off when you do so.
Step 1: Mark your seamline and ¼" inside the seamline
On the wrong side of your fabric where you are going to make the seam, mark your regular seamline (⅝" unless otherwise specified in the pattern) with some tailor's wax or other marking pen. Then, on the right side of the fabric, mark ¼" closer to the raw edge from your seamline (so for a ⅝" seamline, you would mark a line at ⅜").
If you're using tailor's wax, make sure that the regular seam line on the wrong side of the fabric is done in non-white tailor's wax, since you don't want it to come off when you iron in step 4.
Step 2: With the wrong sides together, stitch the exterior (⅜") line
For the plain seam, you're used to wrong-sides out, but because the french seam folds back on itself, we actually start wrong-sides together for this first step. Using a regular, straight-stitch, stitch along the exterior line that you made on the right side of the fabric. (Video after step 3)
Step 3: Trim the seam, clip the curves if necessary
Now we trim down the seam allowance to about ⅛". Don't go right up to the seamline, but you want the allowance to be very slim. If you are stitching along a curve, it's not a bad idea to clip those curves. For more on trimming the seam and clipping the curves, see this post.
Step 4: Iron the remaining allowance to one side and then turn the piece inside-out and iron again
Take the piece over to your ironing board and open the pieces up like you would a plain seam. However, rather than pressing your seam allowances open, you will take the iron and press the seam to one side. It's not a bad idea to pull the side you're ironing towards tight to make sure that you don't accidentally iron a crease in the piece. Once the seam allowance is flattened to one side, flip the piece inside-out so that the wrong sides are now on the outside and iron again, making sure that the seam that you did in step 2 is on the edge of the fold and hasn't rolled in to one side or the other.
Step 5: Stitch along the interior seamline
Take your piece back to the sewing machine and stitch along the remaining tailor's wax mark -- it should be about a ¼- ⅜" allowance depending on how your ironing turned out. Because this can be a variable number, I highly recommend marking this seamline in step 1, since this is the seam that "counts" on the final product as far as measuring and matching up is concerned.
This is just a good idea--I believe the best way to do this is to iron the french seam to the side, although I know some people prefer to iron it flat. I think it depends on what you're making.