There are several methods of abortion.
The pill you refer to is properly referred to as a medical abortion, sometimes called a chemical abortion, using a combination of drugs (mifepristone–misoprostol). This is the least intrusive method and one of the most effective. Essentially, it triggers a miscarriage. As it is performed in the first nine weeks of pregnancy only, it will be akin to a particularly painful and heavy menstrual cycle.
Also, just in case you're wondering about Plan B, it is not an abortifacient. It prevents pregnancy from ever occurring by triggering the menstrual cycle, preventing a fertilized egg (if present at all) from ever implanting. The human body does this quite frequently left to its own devices.
The most common surgical method of abortion is via vacuum aspiration. The cervix may be dilated; either way, the fetal material is removed via a small vacuum. The procedure is relatively safe and more common than medical abortion abortion (roughly 17% medical v. surgical). This procedure replaced dilation and curettage in most countries (particularly the US), but D&C is still performed in locations without access to a vacuum. Basic procedure is similar, but the fetal material is removed via tools instead of a vacuum. It was replaced due to much higher level of risk, cost, and intrusiveness with D&C versus vacuum aspiration.
Before detailing methods of late-term abortion, some context on abortion timing. Some 91% of abortions in the most recent reporting period were under 13 weeks of gestation, per the CDC. Of those, 71% were performed under eight weeks. Later abortions are carried out generally for medical reasons, such as fatal defect in the fetus. Abortion after 21 weeks accounts for less than 2% of all abortions. In these cases, abortion may be elected for a fetus that otherwise would have been willingly carried to term. Viability at its absolute earliest is, with extreme optimism, 23 weeks and becomes somewhat reasonable at 26 weeks (pregnancy is generally about 40 weeks). Lifelong health effects will likely occur in a premature birth, with these risks increasing with earlier delivery. While statistics do not exist specifically documenting the reasons for elective abortions past 12 weeks, it can and has been speculated professionally that the economical and geographical difficulty of obtaining an abortion may be a factor.
These two methods are for first and early second trimester abortions (second-trimester abortions being by far a minority - most abortions are performed in the first trimester). Other methods also exist for later-term fetuses. The following are rarely performed by election. That is not to say it has never happened, but it is rare, and, in the US, virtually impossible without health-related reasons. They are in the vast majority of cases used for the health of the pregnant patient or a fatal defect in the fetus. They are the focus of many anti-abortion activists because they are, indeed, rather gruesome to laypeople. These two methods are as follows.
Intact dilation and extraction, or IDX. Completely illegal as an elective procedure in the United States. Used only to deliver a fetus that is already dead. Ironically, more illegal than dilation and evacuation (which I'll get to in a moment), due to emotional factors. This is what is referred to as 'partial birth abortion'; the fetus is delivered mostly intact. Labor may or may not be induced; at any rate, the cervix is dilated, and the fetus is pulled into the vaginal canal (having been manipulated to sit in the breach position). The head is then reduced in size, generally via vacuum, the fetus is removed the rest of the way, and the remaining material is removed via a vacuum.
Finally, dilation and evacuation. The graphic is not necessarily inaccurate, but was possibly crafted for emotional appeal and use in anti-abortion materials given the age of the fetus shown and the manner of depiction. The procedure is reportedly physically traumatic (although no more than any other comparably invasive procedure) and, given restrictions on abortion and use of vacuum aspiration into the second trimester, rare.
Citations for statistics: CDC - Reproductive Health - Data and Statistics, Guttmatcher Institute - Induced Abortion in the United States.
Feel free to write