You can convert to Islam on two levels.

The convertation on the private leveol is the first and most important step.

Recomended is that you have dealed intensiv with islam. You shopuld ask for everything which is not understod. It is also good to build connection to Muslims who regulary go to the mosque and visit islamic events. By this you get, so Allah will, to the deep conviction that the convertation to islam is the only true ways. The convertation  should be a step of the heart and be done by the deepest conviction. No human can be forced to this as it is said in the Quran: There is no compulsion in religion.

Publically the convertation looks like this: In formt of two witnesses you speak the statment of believe (the Shahada), which is: Aschhadu an la ilaha illa llah, wa aschhadu, anna Muhammadan rasulu llah ("I testify that, that there is no praiseworthy except Allah and I testify that Muhammad is hismessenger“)

 

Convertation from Islam in another religion is not allowed!

Islam, in contrary to other countries, include/ links the believe to God and the existing law for mankind from god. It is not like often in western countries the case that staate and church are beeing seperated side by side but in Islam they both belong together. For a muslim it is the harmony of religion and judical aspect which builds the foundation of his existance and his life. Is the foundation inetionally harmed or attacked the muslim will try to remain it by defending it.
 

Beside this it is an important fact if you regard the freedom of believ according to western measurement or islamic measurement. Both have a complete different background. 

Freedom of believe from the western point of view (Seperationg state and Church) means every one can chose the believe of his choice, live and mission. But is not allowed to violate the judical consitution of the country. You can change your believe at any time and can adopt it according to the way of living.

1. From the islamic perspective freedom of believe means that no one is can be forced into islam. Religious minorities who live in an islamic state should be respected, are allowed to have their religious ceremonies and were in former times even protected by the rulers as long as they did not cause confusions of thinking or violated against the laws in the country.

2. Additionally every human has the freedom to chose his belive and has the right of his own opinion, even an atheist. No one has the right to judge on the believe of some one as long as he keeps it for himself If his thinking which contradict to the believe and moral aspects of the society are spread amonst people to dearrange their minds he violates against the general order. He spreads doubts among the people which can lead to riots.

Every one who behaves like this will be punished. He can even be charged with high treason wich is being punished bydeath but not because he had laid down his believe but because by his spreading of his mind he causes irritation and disharmony in the state and therefore violates against it´s orders.

In westlern couintries punishment is also normal for violating against the judical constitution to ensure state order. These punishments differ from country and states For example you face jail in Germany and in some states of the USA you can face death penalty.

Islam offers another conception of human rights, another than the ones ot the intertnational commities which regard humans as the center of al things. According to islam we realise that human right has Godly nature and that it has it´s legitimation of Allah...

"On the day when We shall summon ill men with their record, whoso is given his book in his right hand such will read their book and they will not be wronged a shred.." (Sure 17,70).

This kind of legitimation certainly is missing in the declaration of human rights by the United Nations, because it is made by men.

An Apostate (read the explanation) is, according to the Quran, only be threatened with punishment in the hereafter. Worldy punishment are relevant when leaving of islam is linked with desertition or high treason. (Violation against the Sharia: applicable law).

Exception:

Worldly punishment is not been executed when the person is not aware of its action, if he was forced to change the faith and if he is mentally instable.

Today there are many countries claiming to be islamic but they do not rule according the sharia and there are also many countries which have a mixture of sharia and human madw laws.

they face when bringing single aspects into existince hugh problems becasue they have signed western human rights constitutions which do not match with islamic human rights constitutions.

The resulting problems appear that these two forms of human rights can not be combined with each other and many of the islamic states do not back up their islamic laws but are letting themslves to be blinded by other values.
 

Because the west is only concentrated on it´s own human right and somehow has less understanding of other forms of orders the islamic way of order is always placed in a wrong light. Due to the unbalanced presentation in the media the wrong perspective is beeing projected to the whole of societys. The advantages of the islamic human rights sadly are totally ignored. As in other judical orders the islamic human rights have to be regarded as a whole. It is always the game that the most extreme is put out to discuss about whithout pointing out the harmony of one islmic community. In order to be objective concerning the human rights in islam you have to regard the single aspects in their context from within and not to judge them from outside

Many experts in the media speak about islam from their western point of view or you see so called muslims who had not even understood their religion nor are they practicing it. So often we the practicing muslims are facing it and can not understand this lack of ignorance or misunderstanding. Without comprehendance of a tiopic from the islamic perspective there will never be set up something as a constructive discussion.

Is it allowed to baptise a child fhich comes from a mixed marriage (the husband is muslim the wife is not)

the children of a mixed marriage between a muslim and a jewish or christian women have to be raised in an islamic way That is why the baptism is not allowed in islam.

Why is it not allowed for muslim women to marry a non-muslim man?

If you bring arguments for the prohibition of a mixed marriage in which a man is a non-muslim and the women is a muslim then you first have to point out that God has ordered it in the Quran: (2:221) "... Wed not idolatresses till they believe; ..." This is pointing towards men who belive in more than one god, so not to jews or christians. (60:10) (über die gläubigen Frauen) "... Then, if ye know them for true believers, send them not back unto the disbelievers. They are not lawful for them (the disbelievers), nor are they the disbelievers lawful for them. ..." The muslim women´s marriage to a man who is not beliving in Islam is therefore prohibitted. He had created us and therefore knows best what is best for us. Woever belives in allah tries to stick to his commandments. The muslim women is not allowed to marry a non-muslim man. The only possibillity is that the man converts to islam. But that should not happen because of the marriage. One imprtant aspect is the granted aspect of performing the religios duties. While the muslim men are ordered by islam to grant their women in a mixed marriage that they can perform religious duties without restrictions by the husbands. The other way round is not being granted to the muslim women by their husband who is from another religion. So the performing of religious duties to muslim women is not granted.

Should converted Muslims take an arabic Name?

You may do this but it is not obligatory. If you want to change it you may do it. It is better to change the name in case if your old namer refers to the old religion, as (Christian, Paul). If this is not the case but you want to find your faith reflected by your name you have the possibillity to enlarge your name inofficially by an arabic name.

Non-muslims in islamic countries

Non-muslims may live in islamic countries. They are regarded as "protected people" (ahlu-dhimma or dhimmi). This means that Allah, his Prophet (s) and the muslim community has made a contract with them, that they may live in security and peace among islam. In modern use of speech dhimmis  are "citicens" of the islamic state. From beginingup to now muslims agree that dhimmis have rights and duties but are free to practise their religion freely. The prohet (s) has pointed out the duties of the muslims towards the dhimmis and threatened every one who violates it by the wrath and punishment of Allah. He said: "who harms a dhimmi has harmed me, has harmed Allah." (Tabarani, in al-ausat, on a secured authority.)

"who has harmed a dhimmi, his oponent am I and whom I was an opponent to I will be opponent on the day of Judgement." (al-Khatib, on a secured authority.)

"On the day of judment will I deal with ever one who opressed one of the people of the contract. or cuts off his right or burden him more than he can carry or takes something against his will." (Abu Dawud)

source : way-to-allah.com