There are a variety of ways to keep a log of memorable contacts (I certainly don't log every one nor those that are routine). ARRL, CQ, Yaesu, and likely others will sell or give away log books to write the pertinent information in. I would guess that Google would turn up a few log sheets, in fact
here is one in PDF right at the top! Programs abound for those who wish to maintain their log on the computer. Very active stations will upload their QSO data to various online logbooks for awards and such.
Even though a number of operating awards can now be obtained electronically, paper QSL cards are still popular and preferred by many operators. The same awards can be applied for with paper QSL cards and that will likely remain so. As for your QSL card, there are a variety of methods here as well. Printers abound who will allow you to make certain customizations to stock designs and sell them by the hundred count and in greater volume. Here again there are computer programs available to design and print a QSL of your design.
Personally, I make my cards using
OpenOffice.org Impress (similar to Microsoft Office Power Point) to create my front and back side of the QSL. I use heavy paper stock and run each sheet through the printer four times (twice front and back) and use a paper cutter to make two QSLs per sheet. The advantage to me is that I can make a special QSL at the spur of the moment or change info on the card without having a run of one hundred wasted when only 15 will be used. The down side is that I don't have a color laser printer so all my cards are shades of gray. I typically make a couple dozen at a run and they last me quite some time.
The QSL card has often been referred to as the "final courtesy" of a QSO. At one time some hams would QSL every contact and some still do a lot of them. Personally, I return QSL 100% as I'm not particularly interested in awards as such but I support those who do.
Hope that helps.