Sustainable gift-wrapping
Reusable shopping bags
These can be easily bought if your time or sewing skills are sparse. But if you want to make them yourself, check out this tutorial on making a bag out of an old pillowcase.
Furoshiki - Japanese fabric wrapping
Generally for this you just need a square of fabric that will fit your gift. There are a lot of different techniques to accommodate different shapes.
For fabric, you can just use scraps from Op Shops with overlockered edges, but you could use bandannas, scarves or plain fabric with unfinished edges if you desire (image below courtesy of Wellington City Council).
Reused wrapping paper
Nothing says frugal like reused wrapping paper! But it isn't just better for your pocket - you are changing it from being single use, to reusable! You might as well get as much life out of each piece of reindeer wrapping as you can!
Recycled brown paper
If you are going to buy anything to wrap gifts, recycled brown paper is a good option; it is the most sustainable way to buy 'new' and there are various ways in which you can re-use it. Re-used brown paper is great for lining your Council food scraps bin (paper linings are not permitted in all regions; check with your local Council).
Second-hand biscuit tins
A pretty tin or reusable box is a practical way to package a gift. Glass jars are also an effective way to present edible gifts such as biscuits or confectionery (just tie a reusable ribbon around the top!). Boxes, tins and jars can then either be used for storage or repurposed for another gift.