Answer by Deepika Razia:

There are three forms of mercury in the environment: elemental, inorganic, and organic (Methy) mercury. All forms of mercury are toxic.

Where do we get exposed to Mercury?
Occupational setting
Inorganic elemental mercury is used in over 600 major industrial plants. The exposure can be via carious routes- via Inhalation (Lungs), via Ingestion or exposure through Skin.

Non-Occupational Exposure in the General Public
Ingestion (Elemental Mercury Vapor)
Standard dental fillings, known as amalgams contain 50% elemental mercury by weight (Nadakavukaren, 2001) which can be released as mercury vapor through normal chewing.
Ingestion (Organic Mercury / Methyl Mercury)
Fish consumption constitutes the largest source of exposure in the general population (Klassen, C.D., 2001). At risk are those who regularly and frequently consume large amounts of fish. So always look for Advisory while buying the fish.

Why we need to worry
Mercury accumulates in various organs of our body because it is highly lipid soluble. It accumulates in Brain, Kidneys, Heart, Lungs, Reproductive Organs etc and causes slow damage over the time, also increases chances of some cancers.

Coming to your question, you specifically want to know about how does it get eliminated from body.
Elemental Mercury- Approximately 7-14% of inhaled mercury vapor is exhaled within a week after exposure. The rest of the elemental Hg is either excreted via sweat and saliva, or is excreted as mercuric Hg. Approximately 80% is excreted as mercuric Hg via feces and urine. Half-life elimination is approximately 58 days.

Ionic Mercury – Approximately 85% of an oral dose is excreted via feces within a couple days. Most of the absorbed ionic Hg is excreted in urine. Smaller amounts are excreted in saliva, bile, sweat, exhalation, and breast milk. Half-life excretion ranges from 49-96 days.

Methy Mercury – The major routes of excretion are bile and feces. MeHg undergoes enterohepatic cycling where it is secreted into bile, and then partly reabsorbed and returned to the liver. Most MeHg is eliminated by demethylation and then excretion of the ionic form in the feces (~90% in feces as mercuric Hg). This process does not occur in nursing infants due to incomplete development; their process of elimination is not understood. Breast milk is also a route of excretion.
The range of half-life elimination has been estimated at 45-90 days (although much faster for lactating females). Individuals who are exposed regularly to MeHg reach a steady-state body burden in about 5 half-lives (~1year).

Here is an article by University of Minnesota which is good one, dose, absorption, distribution, biotransformation and excretion

How does the body remove mercury?