Some seeds will need to be stratified for a period of time. Stratification is when you store seeds in a cold damp place for a period of time to simulate the natural winter period that many seeds go through in nature before they germinate. Basically you should figure that the seeds of a plant will germinate in the same conditions that their parent plant grows in. For many seeds that is a mixture based on peat or live sphagnum moss. The temperature and humidity as well as watering should be around the levels that the parent plants grow in.
Light however is an important factor in seed germination and the growth of healthy seedlings.
Therefore I believe that many types of seed are best germinated under propagator covers and an artificial light source like several cool white fluorescent bulbs. With this set up you can give the seeds as many hours of daylight as are needed, although 16 - 18 hours per day under artificial light is plenty. After the seeds germinate and the seedlings have reached a suitable size they can be separated and grown in small pots in the same soil and under the same conditions of the parent plants. This is the simplest way. However you must wait until the plant has formed 4 - 5 individual plants in the clump.