The best way to get someone into inpatient treatment (while not always possible), is to have a nonjudgmental and open dialogue with the person that you are trying to help.
Most people do not want to go to the hospital, especially when they’re already sick and struggling. If all of your comforting objects, habits, substances, places, and people will be suddenly removed, you logically fear that you will be left with very little capacity to cope. Being put in the hospital can be pure agony, even when you commit yourself.
Try to talk to the person who you think needs inpatient treatment (another way of saying “needs to be committed”) and set up an open understanding that you believe this would be in her best interest, and you want this to be her choice. The most important detail is that you both understand that if at any moment she decides that maybe she should go to the hospital, you guys get in the car and go that minute. Don’t stop to pack, don’t call anyone to let them know, just get in the car and go before she can change her mind. You 
can pack, bring medications, find documents, buy toiletries, and let everyone know later, once she is safe in inpatient care. The best-case scenario that you’re hoping for is for her to have a moment of clarity about needing help or a moment of doubt in her plan to die, and to agree for even just a minute that the hospital is the wisest place for her to be.
To be prepared for this to work well, make sure everyone in her life who could be the person who takes her to the hospital has the name and address of the building they need to take her to and understands the “we go the minute you ask” policy. If you think that packing a go-bag with clothes, books, comfort objects, fidget toys, a small blanket, a journal, and toiletries would make her feel more comfortable with the idea that if she goes, she’ll be prepared, then encourage her to pack a bag. This can help her internalize that the hospital is a real place and she would be cared for there. Standards about what items are allowed in psychiatric inpatient care units vary between facilities, so, unfortunately, depending upon the facility, she may not be allowed to bring all of her things in. In some facilities, she would not be allowed to bring anything in at all. But it can still serve her mental health to go through an act of preparation, and it shows a willingness to go and get help, even if she is very afraid.
If she voluntarily commits herself and tells the staff that she is suicidal, most places in the United States will put her on a 72-hour hold to assess her safety, possibly start her on medication, and begin a treatment plan for her to continue once she’s out. The purpose of the hospital is to provide safety, temporary care, and the beginnings of a treatment plan. There will probably be little to no individual therapy. She will not become healthy overnight. The hope is to try the patient on initial medication, get a diagnosis, and connect them with a psychiatrist, therapist, social worker, and/or case manager who can help them build a care team once they are released. No one comes out of the hospital cured. Some people come out of the hospital way worse. The goal is to start on a path to getting better. But it takes a lot of personal research and self-edification to learn how to manage a mental illness, both for the patient and for the friends and family. Friends and family will be her first-line of support, so read up. This article covers a little bit about being a supportive family member of a mentally ill person. How To Offer Support – Mental Illness – Goldfishpainter
To find a hospital nearby, do a google search with the name of your city and the words “mental health hospital” to find all of the closest facilities to where you live. If she 
chooses to go before you have time to do any research, go to the nearest Emergency Room and let them know she is not safe and needs inpatient care, and they will find the nearest hospital available and make sure she is safely transported there (this is what I know about the U.S., other countries may be different). Unfortunately, this can be expensive.
If you are looking for the legal ways to commit someone involuntarily and you live in the United States, this website will give you your specific state’s requirements and policies for involuntary commitment. In most states, there are three forms of involuntary commitment: Emergency Hospitalization for Evaluation, Inpatient Civil Commitment, and Outpatient Civil Commitment. The Emergency Hospitalization often comes first, when a qualified professional (including therapists, doctors, police officers, and other officials) determines that the patient is not safe. Emergency Hospitalization for Evaluation is sometimes called a “psychiatric hold” or “pick-up.” It only lasts for a fixed period of time, often 72 hours. If the person is not safe after that, on the advice or judgment of an official, a judge may give the order for Inpatient Civil Commitment, meaning that the patient must stay in the hospital until they are no longer a danger to themselves or others. It is also possible to go straight to a judge with an appeal for Inpatient Civil Commitment without going through a psychiatric hold first. Anyone close to the patient who witnesses their behavior can appeal. In most states, a judge can also mandate outpatient treatment, sometimes referred to as “outpatient commitment,” “involuntary outpatient commitment,” or “mandated outpatient treatment.” In most states, a person close to the patient who believes that the patient is in danger has the freedom to file an appeal to a judge to ask for that person to be committed. The above website will have complete information on the legal requirements for commitment in your state.
In the U.S., a person can call the police and report that someone is a danger to themselves, and the police will send out a wellness unit to check on the individual and assess them in person to determine if care is needed. Calling the police, while sometimes necessary, is not the best way to go about things. Sometimes the sick person can talk or act their way out of being judged as a danger to themselves, and the police will leave with nothing having been accomplished to help your family member. Also, if she is assessed to be a danger and she resists the idea of going, she may be restrained, handcuffed, and taken to the nearest facility in the back of a squad car, which can be traumatic.
No one wants to go to the hospital. It’s scary and uncomfortable. She may resent and distrust you for a long time afterward if you involuntarily commit her.
However…
People go to the hospital to get better. That’s what it’s there for. She won’t come out happy, but hopefully, she will be kept safe for a few days and come out with a diagnosis at the very least. Diagnoses are crucial. A correct diagnosis is your family’s first big clue as to how to help her get better. Once you have a diagnosis, you can start researching treatments and get her started with a psychiatrist and therapist. You can learn coping skills for your own mental health and point her in the direction of learning skills herself. You can join support groups that are appropriate to her situation and diagnosis. If she has a substance abuse problem, for example, you can join AlAnon and she can join Alcoholics Anonymous or Narcotics Anonymous. NAMI, the National Alliance on Mental Health, has offices all over the U.S. and offers services that can help build her support system. The more people who actively help or love her, the better her chances of recovery. Her emotions and problems are her responsibility because she is the one who will experience them firsthand (responsibility and fault are different things), but other people are often (but not always) capable of helping. Remember that you can’t save her from herself. But if you take care of your own mental health, you have the potential to help her in some pretty huge ways.
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