There are few medically warranted reasons to induce labor and to essentially send your baby an "eviction notice", and labor induction is a serious act that deserves careful consideration. Some good reasons to induce labor are a pregnancy that has lasted longer than 42 weeks, complications that require immediate delivery like preeclampsia, and the rupture of membranes without contractions starting.
If your healthcare team and you have agreed to induce labor for a medical reason, the next step is to look into the method of labor induction. There are several widely-used medications to induce labor. Pitocin is a drug that you may have heard about, and it is highly effective at inducing labor. Pitocin is the synthetic version of the hormone oxytocin, which plays a role in starting uterine contractions.
Cytotec, a drug that can be used orally or vaginally, is also often used to induce labor. Keep in mind that cytotec was not approved for labor induction by the Food and Drug Administration, and there are possible dangerous side effects (like uterine rupture) that you should discuss with your doctor in advance.
Then, there are also drug-free methods to induce contractions. Sweeping membranes means separating the bag of waters, which your baby swims in, from the uterine wall. A more invasive method to induce labor is breaking that bag of waters (rupture of membranes). If this fails to bring on labor contractions, you will almost certainly be given pitocin.
Midwives use herbal medications like castor oil and blue cohosh to induce labor sometimes, and they can be highly effective but also come with side effects. Finally, there are "old wives tales" about how to induce labor. They include lots of walking, eating pineapple, having sex, eating spicy foods, and standing on your head. You may try these, but don't count on them working!