The question presupposes that sharia law is already in place, so arguments as to the possibility are irrelevant.
I have lived in Malaysia, where sharia is slowly trying to replace constitutional law, it is already in place for Muslims, however currently non Muslims are exempt.
So the first step in introduction is to persuade (if needed) the country to accept that sharia law can be used to settle any matters between Muslims.
Europe is well on the way to that destination.
Next you simply await numeric supremacy in population, and vote it in.
Currently, non Muslim populations are breeding at levels that make it impossible for a nation or culture to exist beyond the next 50 years.
Personally, I figure I would end up dead if sharia law was in place over constitutional law, so would most of you.
There are only a few ways to avoid living in a Muslim state with sharia law holding precedence over non Muslims.
You can change your own constitution to state categorically that no other law than your current statutes can be used in your country, maybe taking the time to declare that America was founded on Christian biblical principals, BUT it was agreed and constituted, that religion and state remained separate and all people had freedom of religion...... you get the drift.
But that freedom also allows sharia law advocate judges to take over your top judicial positions, even the Supreme Court, and eventually, if you keep sleeping, change things to allow for sharia, as has been managed by the liberals over the last 50 years, as they have destroyed family values and Christian principals that founded your legal system.
The problem is that TWO religious cultures are clashing.
On one side there are fundy Islamists seeking to destroy anything non Islamic, who seem to have considerably gained control over both the religion of Islam and the 2 billion folk who adhere to its principals.
On the other side you have equally fundy Christians who are basically living outside of Christian principals, who equally seek to destroy other religious concepts, but who have very little control over the 3 billion Christians (or professing Christians) who are generally to apathetic to do anything except seek a good life and maybe help folk when they can.
Nobody wants to admit the clash, but it's happening, as was predicted, and there is only one result, which will lead to the loss of billions of lives, and end in defeat for ALL the protagonists.