I'm not the most traditional doer of holidays. We didn't eat turkey on Thanksgiving, and I have a Mexican tablecloth playing the role of tree skirt. So it's not shocking that my color choices below are not traditional. If you love red and green, go for it.
I shopped my house for anything I could find to wrap around a gift. I ended up with leftover yarn, fabric trims, and photos.
I then went to the craft store, and bought some acrylic paints and embroidery thread. Both were inexpensive, and had an amazing selection of colors.
I also love some foliage atop a gift, but the last time I did that with Eucalyptus, the cat ate it and got sick, so none of that happening here. But it's real pretty.

Ingredients
Kraft Paper/Butcher Paper
Foil
Photos
Old or Thrifted Sweater Embroidery Floss
Fabric Trims
Baker's Twine
Washi Tape
Yarn
Water-based Acrylic Paints (so you can water them down if they are too thick)
Straws (to blow paint around)
Paint Brushes
Tape & Scissors
VOILA
I'm not going to have a "How To" section, because that would be insulting to my intelligent audience. I will say that if the paint is too thick to fling, water it down. I will also say that trimming down photos can be more interesting than putting the whole picture on top. (Pro Tip: People love photos of themselves.)
Plan B
OR you could just buy some nice wrapping paper. So many amazing options out there... but my quick and easy go to is World Market.