how long does it take a plant to germanate

depends on the plant. some take a few days others months. some seeds need special treatments like chilling, others need warmth, light or no light. the seed packet should give you some idea.

As Mageth says it depends on the plant. do you have any plant in mind?

As Mageth and Seaburngirl says, It depends on the plant and where you have it, warmth is a good germinator, but don't let it dry out.

A caution on Daff's comment there are certain seeds that need a cold spell to start their germination process... reality is Manylok unless you are asking about the process of growing a specific seed it is impossible to answer your question. Peony seeds for example can take two years to germinate. The alpine that David and I grow from seed can take many months to a year to put their noses above the ground. Annuals, i.e. bedding plants should take a matter of weeks... think about it if they took longer than that they would not have time to grown into a flowering size plant and set seed for the following year. Perennials can take much longer.

Lettuce seed germinates within days. We mostly grow perenials and, if they havn't germinated, we keep the seed pots for three years before giving up on them.