The guidance is being made available to colleges and sixth forms
College staff are being urged to be vigilant for students who access extremist material on the internet or use extremist graffiti symbols.
Guidelines are being sent to further education colleges in England to try to prevent students becoming drawn to violent extremism and terrorism.
Skills Secretary John Denham said the "toolkit" would facilitate open debate.
Similar guidelines have already been issued to primary and secondary schools, as well as to universities.
The government guidance caused controversy, with some academics saying the government was asking them to spy on their students.
The government said FE institutions had a particular role to play, as they were often at the heart of local communities and served students from a diverse range of ages and backgrounds.
And ministers believe colleges can play a major role in promoting community cohesion and integration.
'Free and open debate'
The guidelines say colleges must work with their local communities to "develop a resilience" to ideologies that promote hatred and violence.
The guidance says: "Education in a democracy should encourage each issue to be critically discussed and debated on its own merits with proper intellectual and ethical rigour.
"It should also promote the rights of citizens to lawful protest."
The government wants to tackle extremism among young people
The handout addresses how staff and students can create space for "free and open debate" and break down segregation between different student communities.
How to provide support and advice to vulnerable individuals is also addressed.
And the advice reinforces the role of staff in preventing extremism, as well as ensuring campuses are free from bullying and intimidation.
Behaviours and signs to watch out for include graffiti symbols or artwork that promote extremist messages, students accessing extremist material online, parents reporting changes in a student's behaviour, friendships or actions and students voicing opinions based on extremist ideas.
The guidance specifically highlights the threat to the UK from groups influenced by al-Qaeda, which the government judges to be the main terrorist threat at this time.
It also mentions dissident Irish republican groups, as well as some racist and fascist organisations.
'Reflection of society'
Mr Denham said the advice was wide-ranging.
"The tool kit covers guidance about people who seem to be trying to impose their views on others, perhaps through intimidation, or people who might be accessing materials on the internet which look as though they might be illegal or inappropriate."
He said the advice was not meant to suggest extremism in colleges was a major problem, but added that "colleges reflect what's there in the rest of society".
"Whether we're talking about some of the international terrorism that we've seen, whether we're talking about animal rights extremism, because those things exist in a wider society they will turn up in FE colleges."
President of the Association of Colleges, David Collins, said: "College leaders take their role in the community very seriously, so any support in promoting better relations and or help tackling extremist activity is very welcome."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.