It is said on multiple occasions that we need to protect our sanskriti, our dharma, etc.
But is there any reference in our shastras on what should we do to save dharma?
You can not really save Dharma. You can follow it. And, by following it, you're doing what's required of you.
Like, from Devi Bhagavatam 11.1:
Deliverance of one's Self depends verily on his own Self. Therefore one should always earn and store dharma (religion) and observe always there the right conduct to help one in the next world. If Dharma be on our side, this endless sea of troubles can be safely crossed.
So, we can only accumulate Dharma by following the acts that are prescribed for us in the scriptures. Anything else, like saving the Dharma, is beyond our capabilities.
Lord Vishnu, who is the preserver among the Trinities, will look after the protection of Dharma. It's not our job.
As regards, Sanskriti, then in English it's called culture.
So, how can we save our culture is your another question. I don't think you'll get the answer in scriptures.
You can save it by following it yourself. And you can tell your children, family, your friends to follow it. Your children can carry the culture to the next generation and their children to the next and so on. Apart from that nothing is in our hands. Because, we can't really force it on someone else.
The meaning of "SanAtana" is eternal. Which means, "ever existent"-- irrespective of any parameters. Like how "tomorrow never dies", so is the SanAtana Dharma which is ever existent.
One doesn't save Dharma, it's Dharma which saves a person, should one follows it.
Now for every era (yuga), there are localised Dharma-s as well. For example various specific norms of Ramayana era & today's era would be different; they may not apply trivially on each others.
Even such kinds of specific Dharma-s are also upheld by the supreme one viz. God.
BG 4.7 - O scion of Bharata, whenever there is a decline in Dharma and influx of Adharma, then I manifest myself.
BG 4.8 - For the protection of the pious, the destruction of the evil-doers, and establishing Dharma, I manifest Myself in every age.
Since Dharma is auto corrected, we need not worry. We may make a choice however, on which side we want to be among Dharma or Adharma, in any given aspect.
Refer this answer for analogical explanation.
If you were referring to "Hinduism" as "SanAtana Dharma", then it can be saved by increasing more followers by bringing awareness. ISKCON, Ramakrishns mutts, Swaminarayana, various religious Gurus contribute a lot in such aspect.
By protecting it against the influx & influence of other religions is also important. Indian subcontinent is highly successful in that aspect compared to other places in world. Despite being invaded for centuries, still 80% in India are Hindus!
[A] 'Duty towards - understanding and inculcating dharma in yourself and family, following dharma yourself and family' is also "protecting dharma":
(A1) understand dharma( Read saints who have interpreted dharma,darshan and yoga in modern age- like Vivekananda's books,patanjali yoga sutra) And then yourself follow dharma
(A2) help your family/children to understand Sanatan dharma(esp. as a whole) and help them become good follower of dharma and yoga(raj,karma,gyan,bhakti yoga).
[B] 'Duty towards - protecting the dharma follower from adharma follower. Standing against adharma' , - is also "protecting dharma":
[C] Duty towards protecting(within legal framework) the respect of the religion itself, from attacks by malafide forces ( forces which are selectively negative towards 'Sanatan Dharma as religion' due to their own hidden political/religious agendas/biases and not due to some constructive criticism):
Do this to protect Dharma !
Prevent denigration of Deities and patriots that takes place through pictures, advertisements, plays, get-togethers, newspapers, different products etc. ! Refuse to buy products that denigrate Deities and patriots !
To prevent Idol-breaking and thefts taking place in temples, educate trustees of temples and associated villagers !
To prevent the killings of Hindu leaders and Saints, take self-defence training and thereby develop the ability to defend yourself !
Launch agitations against the unjust arrests of Hindu Saints and their subsequent harassment in the prison !
Educate Hindus on the anti-Hindu conspiracies such as attacks on religious processions of Hindu, cow-slaughter and ‘Love Jihad’ !
Legally oppose anti-Dharmik acts such as making of laws like ‘Anti-blind faith Bill’, ‘Temple takeover Bill’, so also the Government policies such as declaring temples as illegal and demolishing them !
Oppose religious conversion of Hindus that is taking place either by luring them or by force !
Lodge complaints(under IPC section 295(A) and/or 153(A)) with the Police against those who unethically criticise Hindu Dharma, Deities, Holy texts, Saints and patriots -, with deliberate attempt to disrespect and demean Hindu dharma. In case of Academic criticism, shashtrarth and meaningful-respectful debate, meaningful-respectful discussion - it should not be applied. Any secular attempt, which attempts to criticize all the religions, movements equally with logic and respect - it should not be applied.
Prevent malpractices such as forcible collection of funds, vulgar dancing, eve-teasing, gambling and consumption of alcohol in religious festivals and fairs !
Common steps in the act of protecting Dharma
A. Education : Educate the individual who is causing harm to Dharma and prevent him/her from causing further harm !
B. Protest : If the act of causing harm to Dharma continues even after attempts to educate, lodge protests in various ways; for example, write letters, send protest messages by fax’or E-mail; contact directly over thephone !
C. Memorandums : Submit memorandums to Government requesting it to stop harm to Dharma !
E. Police complaints : Register complaints with the local Police against the individual/firm for having hurt your religious sentiments !
F. Lawful agitations : If the harm to Dharma continues despite the aforementioned measures, protest in a lawful manner !
If we protect Dharma through such measures with a sense of duty, we will become eligible for God’s grace.
Probably the above list on that website - will vary person to person. But definitely any such activity/protest by anybody, should remain in ambit of civilized conversation and democratic protest and legal/constitutional framework.
First one has to realize Sanatana Hindu Dharma is under attach on multiple fronts, and the attacker are mutating and evolving very quickly. The following needs to be done.
Every individual has a SwaDharma to play to protect the existence of "Sanatanan Dharma". Dharma itself is never destroyed by peoples understanding of it is.
Stop reading and understanding Hindu scriptures from the view of non-followers ... for eg Sheldon Pollock's interpretation of Ramayana and other scriptures
Following a Guru who are integrated to Hindu Shastras, and donot dilute them (not just listening to them on youtube but actually becoming their follower)
By not allowing your ego to build up just coz you have knowledge of some concepts of Vendanta etc but no "real experience"
Internalizing that Hinduism is an organic religion that grows around Gurus (as per Sanskrit definition)
Learning sanskrit (if you can't do it at least your kids or grandkids)
Kids learning in a traditional Gurukul under an "enlightened"/"God realized" Guru for atleast 5 years
Teaching kids to read and write their mother tongue, sanskrit along with english
Going to temples atleast once a week and taking part in its activities
Realizing what your SwaDharma is and then executing it.
Steps 1, 2 and 3 are absolute essential, rest can be done based on ones capacity and capability.
If God exists,It is He who saves the Sanatana Dharma Himself.We can not even save ourselves and dream to save the sanatana dharma? dharmo rakshati rakshitah means dharma saves him who obeys the rules of dharma.
By the way, why would someone even try to save dharma? Love of Dharma means Love of God. So first one has to be mad of God and ready to give up everything to see God. If God gives darshan and orders, only then one can get His power to influence the society.Otherwise how many would listen to him or her?
This was what Sri Ramakrishna said in Kathamrita when He saw Sri Sasadhar Tarkachudamoni trying to save hindu dharma (Kathamrita, Udbodhan, page 469, 25 June 1884.Sri Sitaramdas Omkarnath was also of same opinion (Ref:Omkarsahasralipi, edited by Madhav Ramanujji and Khepar Jhuli, vol 1, by Sri Sitaramdas Omkarnath)