To the venerable Ms. (name withheld) (may Allah protect you from every evil), Please accept from me a good-intentioned greeting!
I was extremely pleased to receive your questions regarding the nature of the relationship between men and women in Islam and how one goes about embracing this religion. I also commend and appreciate your wise and mature sense of judgment in supporting your friend's decision to accept Islam. It shows admirable wisdom and a balanced sense of sagacity and understanding of this blessed event.
Regarding the issue of dating in Islam, one must first define what is meant by "dating." If it is understood to mean how a man and a woman get to know each other for the purpose of marriage, then there are certain guidelines and established procedures which can be discussed. However, if it is understood to refer to casual relationships between men and women who for the purpose of "fun" or "going out" and the such, then there is no provision for this in Islam. Such a situation is not considered respectful for neither the man nor the woman, nor is it constructive for the concept or the building of the family or society or social responsibility. Opening the door to relationships of love and infatuation and passion and pre-marital sex is categorically prohibited in Islam. It does not lead to the establishment of a family nor to proper and virtuous upbringing of children nor to stability and mutual care and tranquility and peace of mind between a man and woman. Rather, it leads to disorder, the disgracing of one's honor and dignity, and to a lifestyle similar to that of animals, and to that of illegitimate children who are subjected to life of vagrancy and loss. (Please see question # 61 which addresses the issue of prohibition of pre-marital relationships).
As for the former case, regarding how a man and a woman come to know each other for the purpose of marriage, it varies from circumstance to circumstance. Normally if a man has the desire to marry and has the ability to accept the responsibility, and he does not have anyone in mind, he will ask his friends, family, and relatives if there is a lady that may be suitable for him and his expectations among their acquaintances and relatives. If someone is suggested, he normally asks about her extensively, about her religious observance, her personality, her knowledge, strengths, weaknesses, suitability as a wife willing to accept all the relevant responsibities, etc. If preliminary information seems appealing, then normally she is told that there is someone interested in meeting her and she is likewise given relevant information about him.
At this point, assuming the man and the woman as well as both families involved agree that there is potential, then the man usually visits the woman's family, often accompanied by members of his own. They are given the opportunity to see each other and sit and talk together, to converse modestly (but not in complete solitude) regarding whatever is relevant to making an informed judgment. The intention for this meeting should be for them to be able to make a decision whether or not they feel are mutually suitable. Afterwards, they each evaluate their own and their families' reactions, and pray to Allah that He guides them to what is in their best interest, and to make them accept the outcome. When both sides feel comfortable and feel they know everything they need to, based on all that has been mentioned such as asking about the other person, knowing their family, meeting in person, etc., they can make a final decision whether to carry on with marriage or not.
As for your second question regarding the procedure for embracing the religion of Islam, it is actually an extremely simple process, without complication or prolongment. This is because it is something between a person and his Lord and there are no other parties involved. All that is required of a person in order to embrace Islam is that he or she pronounce the two testaments of belief in the Islamic creed, believing in their meaning, then to take a complete bath with the intention of (ritual) purification in order to start performing prayers (note to ensure complete cleanliness one should shave pubic and under-arm hair, and a man should be circumcized if he is not already--Islam places great emphasis on proper hygiene and personal cleanliness).
As for the two testimonies of creed, the first is "ash-hadu an laa ilaaha illa allah" (I testify that there is no deity other then Allah), which means that one believes and confirms that there is nothing to be worshipped other than Allah and that one is prepared to implement His divine rulings and guidlines (shari'a) for all aspects of life. The second is "ash-hadu anna muhammad ar-rasool ullah" which means the belief that Muhammad (peace be upon him) is the seal of the prophets (i.e. the final one), whom Allah has sent with the Islamic religion to supercede all other previous religions and that it is obligatory to comply with what he has enjoined, and to abstain and renounce all that he has prohibited and restrained.
I tend to gather from your question that there is a degree of pondering on your part or inclination towards embracing the Islamic religion, joining the example of your friend. I would invite you to carry through with it without excessive delay and reluctance, for one does not know when one's fate will come. So why not meet one's unavoidable fate as a believer in Allah (God) and the Hereafter, a member of the religion of Islam? It is the religion which Allah has specified that He will not accept any other religion besides it, and He will not save anyone from Hell besides its followers. And no doubt that this step will be the greatest thing ever that you will have experienced during your 33 years of life. Surely you will not regret it at all and Allah will help you to surmount the difficulties you perhaps may face in your path after accepting Islam, such as the scorn of some relatives or family members or the alientation of some friends. However, the step in fulfilling your destiny is much more important and significant that all this.
We pray for you to be bestowed with grace, and may Allah guide you to success in what is the most true and right.
Waiting for glad tidings in the near future, may Allah guard and protect you.