Most herbs will be happy growing in water, but those propagated from cuttings are easier to start in water. Seed-grown annuals like cilantro, mustard, and dill are a bit tricky because you need to sow the seeds in soil or some other medium and then transfer the seedlings to water. Soil to water transition is not impossible, but it may not always work out because soil-grown roots are a bit different from water roots.
What you need: Water. Rainwater is best. Do not use chlorinated water. Tap water that has been left to sit overnight will also do. Containers. Water roots like to grow away from light, so tinted containers are best, but not necessary. There are advantages to having narrow mouthed containers which can support your cuttings, but they should by no means be tight. Plant cuttings. You should have about ten centimetres.
Here are the best and easiest herbs to grow: Any type of mint, basil, oregano, stevia, sage, lemon balm, tarragon, thyme, rosemary.