Sidenote: I know that a post like this would be infinitely better with photographs, however, what I have in gift wrapping abilities, I definitely lack in getting technology to talk to each other, so although I took some photos, I have no idea how to get them on to the computer (yes, in this day and age!), and therefore I'll just need to paint that verbal picture. Also, for all of these, I'll leave adding ribbon, bows, tags or other embellishments for after, but think about what you want to go with what – if you have a busy paper pattern, for example, you'll probably want a plain gift tag, and no ribbon.
The biggest tip I can give regarding wrapping is to use enough resources – enough paper, enough room to spread out, enough equipment, enough concentration, enough tape, enough time. Most people that I've seen do a bad job of wrapping presents don't allow themselves nearly enough of these resources.
I have found that by far the easiest place to wrap presents is on a dining table/large desk. Clear it off properly first, don't just bunch the clutter up – but if that really isn't possible, the floor is easier than the bed, in my experience.
What equipment will you need? Obviously, paper. Get plenty of it. More than you think you will need, by about half. Paper is often reduced in January, so you can stock up ready for next year – but make sure you have somewhere to store it where the ends don't get damaged, because otherwise you'll lose any savings in cutting off the damaged pieces. A 12''/30cm ruler is essential, as is a pencil. Tape, obviously, and scissors to cut it if you don't have a dispenser; although with tape, I find that more pieces, shorter in length, works a lot better than trying to get one long piece to behave itself. There's no reason to have a piece of tape longer than about 2'', in my experience. For wrapping certain items, elastic bands (later covered with ribbon) are also invaluable.
My secret weapon for cutting the paper, though? A letter opener! Or use the blade of a long pair of scissors if you don't have one.
Make sure you allow enough time, too. 20-30 minutes per parcel, and if you're wrapping both a box and its lid, count them twice. Break the wrapping up into a few chunks if you can, or at least take regular breaks.
If you can, depending on who else is around in the house and what you need to keep secret, try and separate your wrapping by the type of parcel – oblong or square box; soft items (scarf, jumper, etc); bottles; small, awkwardly shaped items (costume jewellery, chocolate coins); round boxes; boxes with lids that you're wrapping separately; etc, because you'll need a different strategy for each.
For oblong or square boxes, orient the box so that the design on the wrapping paper is the correct way up when the box is the correct way up too. Use your ruler to measure the width of the parcel (in the direction of the roll of the paper), and then divide that in half.
To figure out the width of paper to cut, line up the edge of the box with the edge of the paper, roll the entire parcel over and mark where it gets to with your pencil. Then add on the half value you calculated earlier, and mark that again. Move the present out of the way and extend the line a little – make sure to use your ruler to keep it straight, at right angles to the top and bottom edges.
Turn the paper over (so the pattern is now face up), pull extra out and fold it back on itself. When you see the second mark you made, fold the paper down and use the edge of your ruler to make a smooth crease. Use your letter opener or the blade of your long scissors to cut along the crease between the two layers.
Move the roll of paper out of the way, and repeat the process for the other direction, but you don't need to add on the half measurement.
Widthways, bring the paper about ¼ of the way across the present and, if possible, tape the paper to the present. Roll the present tightly in the paper, making the corners crisp, and tape down starting in the middle and working outwards. This should also be about ¼ of the way across the present.
For the edges, there should be just enough paper to cover the length of the box, with no excess. Orient the present the correct way, press the paper at the edges down, making sharp creases down the sides. Fold the sides in and the bottom (which should be a perfect triangle by now) up, and make sure to fold both sides before you tape either – this is the key to getting them to look neat, and adjust them if you need to.
For soft parcels, the process is similar, but because they don't really have a 'depth' the way oblong parcels do, you will need to add extra paper on to the height when measuring from the bottom to the top of the paper – an extra 5cm/2'' should be enough. Just make sure that when you fold the triangles up, you leave a small gap (1cm) between the present and the fold. I don't really know why this matters, but it really makes a difference if the fold isn't right next to the present for soft items!
For bottles, the easiest way to do it is if you're sending two: pull out a long length of paper, lay the bottles across the long edge neck to neck, with a large gap between them. Roll up across the height of the paper (or part of it), fold in and affix the ends, and then carefully twist the bottles away from each other, and bring them down next to each other so the twisted paper makes a handle. Then just tape the two bottles together for stability and the job's a good'un.
For just one bottle, and for small awkwardly shaped items, the technique is the same, but use different sizes of paper. Cut two squares that are each big enough to wrap the gift, and lay them on top of each other at an angle. You could use three layers, but that may be bordering on wasteful. Put the item in the centre and gather the paper up around it; secure with an elastic band. To make this easier, wrap the elastic band around your finger a few times, and then slide over the edges of the paper, rather than trying to loop it over multiple times, which is likely to tear the paper. Then poof out the top bits until it looks nice – make sure they top pieces are not too short. This technique looks especially good if you use tissue paper for the inside layer and wrapping paper for the outside.
If you have something long and thin like a pen box that would be fiddly to wrap up as an oblong, or you have any kind of tube, the best way to do it is as a Christmas cracker. Wrap the length of it as you ordinarily would, but leave plenty of room at the ends (the exact measurements will depend on the size of the parcel). Secure with elastic bands as above.
For a round item (a tin of biscuits, that cake tin I mentioned), cut a very large square of paper, put the item in the centre and bring diagonally opposite corners in and tape; there should still be room between the item and the paper at this stage. Once the corners of the paper have all been brought in, repeat with the corners of the new shape, to give a square parcel.
To wrap up a box with a lid, it depends on if you only want the outside wrapped up (do it like an oblong box but only include enough paper for the three sides you want to cover, and the same with the lid), or if you want to wrap up the insides too. In that case, the technique I recommend is the one shared by Jen at I Heart Organising in this post on drawer dividers: http://www.iheartorganizing.blogspot.co.uk/2013/01/diy-cereal-box-drawer-dividers.html
This would also work to wrap up boxes with lids that do not have right angle corners, I think – just use multiple strips, and overlap them.