Are there effective ways to purify the liver?

Non in allopathic. In allopathic medicine there is no medicine to do it. If the pt. Has alcoholic hepatitis then stop alcohol intake helps. If certain medicine is increasing the liver enzymes then stopping them helps. Some intoxications have their own antidote. Once the liver has fibrosis in it, there is no curable treatment except transplant. What is a "toxic liver" for non allopathic physicians is a theme of debate.
Liver is purifier. The liver and kidneys are the purifiers of the body, processing and eliminating toxins; healthy liver does not need detoxification. Milk thistle can help a sick liver; increases glutathione, used by liver for detoxification. Best measure is avoid liver toxins eg alcohol or too much acetaminophen. Some nutritional substances contain plant materials harmful to the liver -- do research before taking.
Dietary modification. Human nature tries to focus on possible short term remedies (1-2 days) to counter the 363 days that we treat our bodies less than perfect. The best way to a happy liver overlaps with healthy living in general: 1) eat right and limit highly processed food, 2) exercise so that you process calories efficiently, 3) find ways to deal with or minimize stress, 4) drink alcohol in moderation, 5) get sleep.
Liver detox. Each organ can be cleaned a specific way - nac resets liver along with livotrit which had ayurvedic herbs and milk thistle - biotics had liver detox called 3 step detox works very well.
NAC. Nac re-energizes liver for complete liver detox follow biotics 3step detox system.