Governors should join teachers for Inset days and become "specialists" in areas of the curriculum, according to an Assembly report.
The cross-party enterprise and learning committee said governing bodies need to understand education policy and national schemes such as those to reduce child poverty.
Its report made 21 recommendations on the work of Wales's 23,000 governors, including "serious consideration" of compulsory training for chairs, vice-chairs and new recruits. It also said aspiring heads should receive training on governance as part of the National Professional Qualification for Headship.
Governors Wales welcomed the report and agreed governors should know about national initiatives.
Jane Morris, its director, said shared training sessions with school staff can be extremely beneficial.
"The importance of inviting subject leaders to make a presentation at governing body meetings is equally valuable," she said.
Governors Wales also supported the recommendation of a quality mark for governor training, but warned it would have to be flexible and accessible to all potential candidates. The body is already working with several local authorities on a governor accreditation scheme.
But committee members said governors' effectiveness as "critical friends" of a school would ultimately be proven by long-term improvement in pupils' grades.
According to the report, the best governing bodies have been well trained and received support from the school's head.
The committee had previously reported on the teachers' workload deal, which highlighted weaknesses in the relationship between chairs of governing bodies and heads.
Mike Maguire, Estyn inspector and former head, told the inquiry committee that governors should ask to join staff on Inset days, see samples of pupils' work, probe teacher assessment data and review policies regularly.
Chris Jones, Cardiff City Council's director of education, said: "The most important additional responsibility that has been put on (governors) is the focus on monitoring standards. We have to persuade governors who have an intense loyalty and commitment to the school and community to remember that they are critical friends - not just friends."
Experts told the committee that heads had a responsibility to make school information more transparent and ensure governors' voices are heard.
Mr Maguire said new heads should be trained in how to work with governors. "We find in some governing bodies, heads don't provide governors with sufficient in-depth information for them to really make relevant decisions," he said.
Mr Jones said the governing body's relationship with the headteacher was often the last issue taken into account in governance.
He added: "There is an anxiety that when people become heads, they immediately have to work with governing bodies and sometimes their experience of that is limited."
He said deputies should be encouraged to get involved with the governing body and share the burden of governance - such as sub-committee meetings - with heads.
In June, education minister Jane Hutt revealed Assembly government plans to allow schools to federate their governing bodies.
Officials giving evidence to the inquiry committee were broadly supportive of the measure. But at a meeting in June, Assembly Member Gareth Jones, the committee chair, said: "Sometimes I wonder if we are asking too much of our governors."