Accurate cutting will make a nice difference in your finished project, but it is really kind of impossible to cut things out perfectly. But don't worry, you can neaten them up after cutting & interfacing.
If you are using fusible interfacing, it is best to true your pieces AFTER you apply the interfacing. The process of affixing it to your fabric often changes the shape of your fabric piece slightly.
You don't need to true up every piece. I true only the focus fabric pieces for any flap piece (Curvy Clutch, Envelope Clutches) or pockets/pouches with curved top edges (i.e. Cell Phone Case, Fold-Over Clutch).
Here is how to true your pieces:
Realign the Fabric Fibers
At this point, the piece is cut out and fusible interfacing has been applied to the WRONG side. The piece is totally cooled off so the interfacing is set in place.
Gently stretch the piece on the bias in both directions. Just give it one firm, but gentle, stretch along both bias grains.
Then gently stretch the piece along the cross grain (width).
Smooth your piece down flat on your work surface. If it isn't laying flat, give it a quick press with the iron.
Trim Curved Edges
Fold your fabric piece in half along the grain, but don't make a crease down the center. Match up the edges.
Take a look at both sides and see if the main curves are identical. If you see some extra fabric peeking from behind, trim it off.
Follow the Trued Edge When Sewing
When you are sewing, place the trued piece on the top, so it is the piece directly under your presser foot. Sew the pieces together, using the edge of the trued piece as your guide.
So on my pieces, the lining might be sticking out past the edge of my trued focus fabric piece, but I just ignore it and follow the edge of the focus fabric piece.
