You need only a very weak detergent solution for washing emulsion surfaces - 60 millilitres (ml) (4 tablespoons) of soap in about 5 litres (a gallon) of hot water. Any multi-purpose liquid cleaner is fine. You can buy cleaners sold either as liquids or as highly concentrated liquids (follow the dilution directions on these). Choosing one with a mild fragrance can make the task more pleasant. With this mild mixture, hand irritation shouldn't be an issue, so you may want to wear cotton gardening gloves to absorb extra water rather than hot and heavy rubber gloves. Sugar soap washes walls well too but is much more expensive than the detergent you use for occasional cleaning. Save the sugar soap for special occasions such as when you're about to repaint and want to remove all trace of detergent residue.
I find a sponge mop best for washing ceilings. For stubborn spots, you can tie a towel over the mop to get added rubbing power. When washing down walls, you can get closer using a sponge (an old natural sponge that's too tatty for the bathroom works well).
Whether you're using a mop or sponge, keeping it well wrung will help prevent streaks.
Give yourself a clear area for working, thus avoiding tripping over whilst working. Move electrical items well out of the way, or anything else that may be upset by dripping water. The first step in cleaning is dusting to remove the light surface dirt. Using brushed lambs-wool is perfect. In cleaning a ceiling, start by imagining you're on a cleaning task you do often such as mopping the kitchen floor. Take your mop or sponge right around the perimeter, going tight into the corners where the ceiling is likely to be dirtiest. Wring out your mop or sponge, dip it into your cleaning bucket, wring again, then work across your ceiling in quarters, going backwards and forwards in lines in each section. If your ceiling is such a height that you need to stand on some steps, you may find it easier to imagine you're tackling a chessboard of small squares. Avoid long mop strokes that could cause you to overreach and overbalance.
To wash a wall, start at the top of the wall and work your way down. That way, you can wipe away drips that run away from you. I suggest that you first wash the top along the whole length of the room - this is the tiring, stretching bit. Next, divide the wall into manageable vertical sections. Then, for each section, do the skirting board (baseboard), and a few centimetres (inches) of wall directly above it, as this is dirtier and takes longer to get clean.
Next, look for any particular stain problems and marks on the wall, and tackle them - around the light switches may be especially grimy. If necessary, spot clean these with a drop of neat multi-purpose cleaner on your sponge. Then, it's on to the easy bit that you can whip through - the middle section of the wall. Work along in easy up-and-down sweeps, overlapping slightly with the top and bottom sections that you already washed.