How a simple Muslim (not an Islamic Scholar) who is living in a Muslim country can contribute towards the act of Dawah (proselytizing or preaching of Islam)?
This answer is largely based on the content of this article: The companions and da'wah by Dr. Raghib Al-Sergany. Since your question is focused on proselytization, the simple answer is:
- to recognize that it is the duty of every Muslim, within the guides of their knowledge level
- to convey the message based on knowledge, even if limited, and
- to follow the footsteps of the prophets, and their companions (methodology of passing the message).
Da'wah is every Muslim's duty
Allah (ﷻ) tells us that the best words are the ones for the purpose of da'wah, demonstrated by actions that fortify the message, and to do so with the right intention (driven by Islam):
وَمَنْ أَحْسَنُ قَوْلًا مِمَّنْ دَعَا إِلَى اللهِ وَعَمِلَ صَالِحًا وَقَالَ إِنَّنِي مِنَ المُسْلِمِينَ
And who is better in speech than one who invites to Allah and does righteousness and says, "Indeed, I am of the Muslims."
The Prophet (ﷺ) reiterates this very important message in an authentic (sahih) hadith that teaches us to be honest about the message that we convey, i.e., focus on the quality of the message, even if the quantity is so little (one verse):
بَلِّغُوا عَنِّي وَلَوْ آيَةً، وَحَدِّثُوا عَنْ بَنِي إِسْرَائِيلَ وَلاَ حَرَجَ، وَمَنْ كَذَبَ عَلَىَّ مُتَعَمِّدًا فَلْيَتَبَوَّأْ مَقْعَدَهُ مِنَ النَّارِ
Convey (my teachings) to the people even if it were a single sentence, and tell others the stories of Bani Israel (which have been taught to you), for it is not sinful to do so. And whoever tells a lie on me intentionally, will surely take his place in the (Hell) Fire.
Da'wah must be based on knowledge
While we were all expected to participate in da'wah, it is crucial that we do so based on knowledge, even if the knowledge is limited to a few topics only or even one topic:
قُلْ هَذِهِ سَبِيلِي أَدْعُو إِلَى اللَّهِ عَلَى بَصِيرَةٍ أَنَا وَمَنِ اتَّبَعَنِي وَسُبْحَانَ اللَّهِ وَمَا أَنَا مِنَ الْمُشْرِكِينَ
Say, "This is my way; I invite to Allah with insight, I and those who follow me. And exalted is Allah ; and I am not of those who associate others with Him."
Topics to cover in da'wah
Adjust the content and the pace of the message to the audience. In the following authentic (sahih) hadith, the Prophet (ﷺ) is advising Mu'adh ibn Jabal how to do da'wah to the Christians of Bani Najran. The Prophet (ﷺ) showed Mu'adh that the first step is to explain the pillars of Islam one by one, in order, and not to proceed from one to the other before the one being discussed is accepted, and to do so in very strict adherence to being just and avoid any form of transgression:
إِنَّكَ سَتَأْتِي قَوْمًا مِنْ أَهْلِ الْكِتَابِ، فَإِذَا جِئْتَهُمْ فَادْعُهُمْ إِلَى أَنْ يَشْهَدُوا أَنْ لاَ إِلَهَ إِلاَّ اللَّهُ، وَأَنَّ مُحَمَّدًا رَسُولُ اللَّهِ، فَإِنْ هُمْ طَاعُوا لَكَ بِذَلِكَ فَأَخْبِرْهُمْ أَنَّ اللَّهَ قَدْ فَرَضَ عَلَيْهِمْ خَمْسَ صَلَوَاتٍ فِي كُلِّ يَوْمٍ وَلَيْلَةٍ، فَإِنْ هُمْ طَاعُوا لَكَ بِذَلِكَ، فَأَخْبِرْهُمْ أَنَّ اللَّهَ قَدْ فَرَضَ عَلَيْكُمْ صَدَقَةً، تُؤْخَذُ مِنْ أَغْنِيَائِهِمْ، فَتُرَدُّ عَلَى فُقَرَائِهِمْ، فَإِنْ هُمْ طَاعُوا لَكَ بِذَلِكَ، فَإِيَّاكَ وَكَرَائِمَ أَمْوَالِهِمْ، وَاتَّقِ دَعْوَةَ الْمَظْلُومِ فَإِنَّهُ لَيْسَ بَيْنَهُ وَبَيْنَ اللَّهِ حِجَابٌ
Narrated Ibn 'Abbas: Allah's Messenger (ﷺ) said to Mu'adh bin Jabal when he sent him to Yemen. "You will come to the people of Scripture, and when you reach them, invite them to testify that none has the right to be worshiped except Allah and that Muhammad is His Apostle. And if they obey you in that, then tell them that Allah has enjoined on them five prayers to be performed every day and night. And if they obey you in that, then tell them that Allah has enjoined on them Sadaqa to be taken from the rich amongst them and given to the poor amongst them. And if they obey you in that, then be cautious! Don't take their best properties (as Zakat) and be afraid of the curse of an oppressed person as there is no screen between his invocation and Allah.
Keep in mind that the major message of da'wah is always on the belief in Allah, doing the right things (halal), and abandoning the wrong things (haram), and to demonstrate belief through actions (salah, zakah, etc.):
وَالْمُؤْمِنُونَ وَالْمُؤْمِنَاتُ بَعْضُهُمْ أَوْلِيَاءُ بَعْضٍ يَأْمُرُونَ بِالْمَعْرُوفِ وَيَنْهَوْنَ عَنِ الْمُنْكَرِ وَيُقِيمُونَ الصَّلَاةَ وَيُؤْتُونَ الزَّكَاةَ وَيُطِيعُونَ اللَّهَ وَرَسُولَهُ أُولَئِكَ سَيَرْحَمُهُمُ اللَّهُ إِنَّ اللَّهَ عَزِيزٌ حَكِيمٌ
The believing men and believing women are allies of one another. They enjoin what is right and forbid what is wrong and establish prayer and give zakah and obey Allah and His Messenger. Those Allah will have mercy upon them. Indeed, Allah is Exalted in Might and Wise.
The methodology of da'wah
There is no conclusive list compiled that I know of. These are some situations from the seera to demonstrate how da'wah was conducted during the time of the Prophet (ﷺ).
Start with people who are close to you
The Prophet (ﷺ), when first inviting people to Islam, he started with those who were closest to him: his wife Khadija bint Khuwaylid, his closest friend Abu Bakr Al-Siddiq, and his closest blood relative and his cousin 'Ali ibn Abu Talib.
Abu Bakr Al-Siddiq, once he embraced Islam, and all he knew about Islam was Al-Shahadatayn (the testimony of faith), he immediately embarked on inviting the pople close to him at the time. That very same day of his Islam, he got 'Uthman ibn 'Affan, Al-Zubayr ibn Al-'Awwam, Sa'd ibn Abi Waqqas, Talha ibn 'Ubaid Allah, and 'Abdul-Rahman ibn 'Awf to embrace Islam. On the following day, he got Abu 'Ubaida ibn Al-Jarrah, 'Uthman ibn Madh'oon, Al-Arqam ibn Abi Al-Arqam, and Abu Salama 'Abdullah ibn 'Abdul-Asad to embrace Islam.
As you can see, the Prophet (ﷺ) invited those close to him, who in turn invited those close to them. The success in da'wah greatly depended on the amount of trust between the inviter and the invitee; but most importantly, the relentless effort put forth.
Pass the message with conviction
الله ابتعثنا لنخرج من شاء من عبادة العباد إلى عبادة الله، ومن ضيق الدنيا إلى سعتها، ومن جور الأديان إلى عدل الإسلام، فأرسلنا بدينه إلى خلقه لندعوهم إليه
— NOTE: My own translation, so treat with care:
Allah sent us to get whomever He wills from the worship of Allah's slaves to the worship of Allah, and from the narrowness of this world to its vastness, and from the injustice of religions to the justice of Islam. He sent us with His religion to his creation to invite them to it.
The message delieverd was clear, concise, and vigorous. This is what caused Rustam to ask his advisors afterwards if they had heard any speech that was more precious or logical. This story also teaches us da'wah, although it starts with prophets and messangers, it does not end there. We all have our own duty to fulfill.
Be gentle in passing the message
It is easy while trying to be vigorous in passing the message to go over and end up repelling people from listening to the content of the message. This is what happened initially with Al-Tufayl ibn Amr Al-Dawsi.
Al-Tufayl is from the chief of the tribe of Banu Daws. Right after embracing Islam, while his knowledge was very limited about the religion, he went bacl to Daws. His father was the first one he met. Al-Tufayl told his father that he would stay away from him long as his father did not accept Islam. His father agreed to accept Islam. Al-Tufayl repeated the same thing with his wife, and she, too, embraced Islam. Al-Tufayl extended this method of invitation to the rest of his tribe, but in this case, the tribe elected to stay as disbelievers, and to replace Al-Tufayl with another chief of tribe.
Al-Tufayl went back to the Prophet (ﷺ), and asked him to curse Banu Daws. The Prophet (ﷺ) asked Allah (ﷻ) to guide Daws and to bring them to him (see Sahih Al-Bukhari 80/92). Then the Prophet (ﷺ) asked Al-Tufayl to go back to them, to invite them, and to be gentle in the way he invited them (ارْجِعْ إِلَى قَوْمِكِ فَادْعُهُم وَارْفُقْ بِهِم). He did, and Banu Daws did indeed go the Prophet (ﷺ) and declared their Islam. Among those who embraced Islam through Al-Tufayl was Abu Hurairah, the most prolific narrator of hadith.