Older wiring had red insulation for the live line, black for the neutral line and green for the earth wire. Newer wires conform to a European standard.
If you have a 13 amp plug with a fuse, the live wire may connect under or alongside the fuse. The neutral terminal (marked N) is at the other side. There will be a flex-retaining clip at the entrance to the plug. This takes any strain, instead of it being transferred to the terminals. Make sure the outer casing will go under that clip when the wires have been cut to length.
If the wires go around screws, wrap them in the direction of tightening. Make sure there are no loose strands. Tighten the re- taming clip and re-assemble.
At the other end of the cable, connections to an appliance are generally similar, but the outer insulation may have to be cut back more to allow a spread of the wires. Connect brown or red to the terminal marked L and black or blue to that marked N. The earth connection will probably be to an unmarked screw in the casing or a metal part. See that any strain on the cable will be taken by a flex retaining clip and not by the electrical connections.
For a lamp socket connected with twin flex, pull out the plug or switch off the mains, then check how the electrical connections are relieved of load. Usually they loop under a central plastic part and the cover screwing down may further tighten them. Do not bare any more of the ends than are needed to fit into the screwed ends of the contact plungers.
To wire a table lamp with a siivitch built in, make sure it is the live (brown or red) wire that goes to the switch. The other wire goes to the lamp holder. If a torpedo-shaped switch is to be put in the flex, cut the live wire and bare its ends. The other wire will go straight through the switch casing. Adjust the amount of the live wire ends used to make connections to the switch, so there is equal tension on both parts of the cable when the switch is assembled.