Whenever I'm taking pictures to make a new pattern I sometimes catch myself pinning my fabric pieces with the pins running parallel to the edge of the fabric. This is how my mom always pinned her fabric so it is just kind of ingrained in my head that way. Then I take them out and put them in perpendicular to the fabric edge because they show up better in photos and in some respects is is easier to sew with the fabric pinned that way.
There is really no right way to pin--at least in my opinion--but here are three different ways to fasten fabric together while sewing and when you might want to use each method.
1. Pin Parallel (Vertical)
When you are cutting a pattern out this is usually the way you want to insert the pins on the pattern pieces so they aren't in the way of the cutting edge. But there is also a very good reason why you might to use this method to pin your fabric pieces together--to avoid pin holes!
Some fabrics never really heal from having a pin stuck in them and the pin hole can be surprisingly obvious. By pinning parallel to the fabric edge and close enough to the edge so you are within the seam allowance you can avoid permanent pin holes.
2. Pin Perpendicular (Horizontal)
Inserting the pins horizontally will make it fast and easy to remove the pins while sewing. If they are inserted fairly straight you can also just sew right over them. Some people say not to do this, but my high school sewing teacher advocated sewing right over them. I do remove most of them just out of sheer habit, but the times that I've sewn over them it has worked fine.
3. Use Binder Clips
I blogged about this last year right here. This is my favorite way of holding together thick layers of fabric or things that need to be kept really flat while sewing. For example on the Business Card Wallet & Checkbook Wallet patterns the pockets work best if they are kept as flat as possible against the lining piece while sewing. Pinning bunches up the fabric and just that small amount of give can make the pocket not lay perfectly flat.
When using binder clips they sometimes catch just a little on sewing machine as the fabric feeds and they come up onto the sewing machine arm. I've never had one get stuck but sometimes it gives me a start if I'm zoning out and mindlessly sewing along.