For inspiration, check out this gallery of completed lamps.
Step 1: What you need
* wire cutters/strippers or an old pair of scissors
* small flat head screw driver
* an old phone charger
* a couple of 150ohm resistors
* a couple of LEDs
* a chocblock
* something to make the base with; we now use sections of old carpet tube but we've used cans and plastic bottles before.
* a 20cm length of stiff but bendable wire
* (optional) 3 shorter lengths of wire for making legs
* some sellotape
* some 200gsm paper for the shade, about 30x40cm is good, a little less than a3.
Step 2: (optional) solder leds onto resistors
Otherwise, you can work out what size resister to use with Ohm's law. V = IR. Let's work out what resistor size we need for an LED with a forward voltage of 2.5V and a current use of 20mA. The phone charger provides around 5V, but can vary so if you have a multimeter you can test it.
Subtract the forward voltage from the phone charger supply to get the voltage over the resistor = 2.5V. Then work out R = V/I = 2.5V / 20mA = 125Ohms.
It often works to just put the LEDs in series, so that the voltage is divided across them both. To do this, twist together the long leg of one LED with the short leg of the other, then test with the phone charger and check that they are not too bright or too dim.
For more info on serial vs parallel circuits, see the wikipedia page here.