Dead-heading is much less brutal than it sounds! Basically flowers are a plants way of having sex! Plants produce flowers in order to attract insects who will either bring pollen from another flower to them or take their pollen away to fertilise another flowers. Once successfully fertilised, the flower starts to make baby plants - seeds. Have you heard to expression "going to seed" - often used by people about people - and often in a negative context? Well this is where the expression comes from. If a plant goes to seed then it stops flowering and put the energy into growing those seeds, so if you remove the old flower heads once they've 'gone over' or 'died' then rather than producing (going to) seed the plant will produce more flowers to try are attract more pollinators. To dead-head just using your fingers is enough on many plants, like cosmos, with thin snap-able stems. Scissors are useful with petunias and fleshy stems that'll get sticky and secateurs for tougher plants like roses, cut the stem below the flower head and if the flowers on a long stem cut the stem back to the first leaf.
All that said- sometimes you need to leave the flowers to go to seed as its the seeds you want - notably fruit - blossom is the flower but you don't deadhead blossom because its the seed (albeit inside a fruit) that you grow the plant for.
It's also worth knowing that bulbs are different again, the bulb actually stores the sugar (energy) that will help the plant regrow the following year so although it's OK to remove a flower stem when it's 'gone over' but leave the foliage as its making the sugar (remember photosynthesis?) to help next year's growth.