How did pagan customs get into Christianity?

 Because christianity tried to replace and suppress paganism.By adopting  their religious festival times put simply.

The Trinity doctrine isn't as "pagan" as you'd like us to believe. Just as Christianity is based in the prophecies of Judaism, the Trinity doctrine is firmly rooted in the Torah also. Deuteronomy 6:4,5 brings support to Matthew 22:37. See also Psalm 51:11 and Proverbs 30:4.

 They were practices too dear to the people, customs too deeply rooted and intertwined in the public and private life of the ancient world. The mother church, kind and wise, did not believe that she had to uproot them; rather, by transforming them in a Christian sense, raising them to new nobility and new life, she prevailed over them by means that were powerful yet gentle, so as to win to herself without uproar the souls of both the masses and the culture.

Pagans were PEOPLE. The first Christians had been pagans or Jews before they became Christians. Christians were not some new physical species unrelated to the people before, they WERE the people before. Modern day people do not understand the NATURE of paganism, and imagine it was a different theology. In fact, it was pretty much nothing more or less than observations of nature--including human nature--which are always universal and true. They EXPRESSED it in symbols such as stories of gods and goddesses, but those were personifications of things like LOVE, which was very much physical love to them. Then you had things like the ocean seen as a god of the sea, which was in fact the sea itself. And a moon goddess, which was the moon. The world was the planet risen to consciousness. All of those things still exist, we just describe them differently and, in the case of human sexuality, had been taught to fear it. But it remains essentially unchanged. The repression of sex has not eliminated it, just made it a source of madness. There are still crops, seasonal cycles, and so on, and those were ALL observed by pagans centuries before there was any concept of PEOPLE being "pagans" as opposed to simply being people. Until there was such a concept as non-pagan, people did not know themselves to BE pagan. It was merely being a human. Nudity had never been shocking. Sex had never been dirty. Sex and aspects of sex were symbolised as gods. So were other aspects of nature. Nature and Nature's God. 

It is true that many pagan religions (before and after the time of Jesus on Earth) had triads of 3 gods (usually with a goddess). Whatever is of God, Satan mimics and distorts. Do pagans pray? Do pagans worship? Do pagans have special celebrations? Do pagans try to convert others to join them? Do pagans misrepresent God's truth so as to bring Jesus down a peg or two? All pagan versions of what God calls His people to do are corrupted by paganism and especially regarding the Being of the one God. That is why the N.T. warns to stick to the teachings delivered, once for all, to the Christian saints (Jude vs. 3). Beware 'new' teachings (especially, for us, ones introduced in the 20th and 21st centuries.) So - is the Trinity doctrine pagan? How far back can we trace discussion of it? Some claim it only arises in the 4th century, which would make it a new teaching and to be avoided at all costs for that reason alone!

Well, the Council of Nicea (in AD 325) was called to bring an end to a dispute that had been gathering momentum since the end of the first century AD – culminating in Alexander and Arius 'battle' on the person of Christ. Yet Tertullian (AD 160-230) had done major spade-work to express Trinitarian belief A CENTURY BEFORE ARIUS! The Nicene Council formed a creed to prevent people like Arius wheedling their way around statements of belief so as to maintain their positions in the Church, when they were actually teaching heresy about Christ. The Council was proof that the debate had been going on for some 250 years!!! JWs never, ever admit that fact.

The Council decreed that anybody who could not agree with this formula would be anathema – cursed: it said that the Son of God was “true God of true God, begotten not made, of one substance with the Father.” Trinitarianism was implicit in Christianity from the beginning; it is only its explicit formulation that took a long time to develop. 

Today we have several groups refusing to believe that the Son of God is uncreated – that he was never ‘made’ but is eternal. They also disbelieve Jesus being of the same divine substance as the Father. Those people keep slinging mud at the Nicean Council and Creed because they are the modern-day counterparts of Arius. And they know it. So they misrepresent the long-running debate about the Trinity doctrine. They try to imply that it was just a handful of men who made a proclamation hundreds of years after Jesus’ death, that wasn’t biblical, and that wasn’t supported by the majority of Christians.

JW belief in angels is actually pagan, for they claim the Son of God was a created angel (as did Arius). Their 'Bible Teach' book (hidden away in the Appendix on page 218) says of the Archangel: "Michael is another name for Jesus Christ, BEFORE and AFTER his life on earth." There's paganism for you! Now go read Rebmilc's excellent answer.

They appropriated them to help people transition from local religions to Trinitiariansim.

The Trinity has never been a teaching of Christianity. If anything, Trinitarianism accepted many Christian teachings. Charity, compassion and love were embraced but they kept much of their violent teachings such as war, terrorism and hate.

The Trinity man-god is a hateful god. It is nothing like Jehovah or his son Jesus. 

Peter Gore Seer,

 It Should Read,  Why Did Christianity Steal Pagan Grounds, And Altar Rituals,

Soon after Jesus finished teaching the Gospel, the anti-Christ came and planted his words so close to Jesus' words that his words can not be removed without uprooting Jesus' words: Theophilus, Luke, and Paul, contaminated the Gospel by changing Mark and Matthew's Gospel then adding their own gentile scriptures.

antichrist originally meant "substitute" or "instead of".

How? It got into Christianity when Jesus Christ clearly taught about it. The Bible repeatedly mentions the Trinity. A few examples:

Matthew 28:19 - Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: (FATHER, SON, HOLY SPIRIT)

Matthew 3:16-17New International Version (NIV)

16 As soon as Jesus was baptized, he went up out of the water. At that moment heaven was opened, and he saw the Spirit of God descending like a dove and alighting on him. 17 And a voice from heaven said, “This is my Son, whom I love; with him I am well pleased.” (FATHER, SON, HOLY SPIRIT)

2 Corinthians 13:14 - The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Ghost, [be] with you all. Amen. (FATHER, SON, HOLY SPIRIT)

John 14:26 - But the Comforter, [which is] the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you. (FATHER, SON, HOLY SPIRIT)

1 John 5:7-8 - For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one. (FATHER, SON, HOLY SPIRIT)

John 14:16-17 - And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever (FATHER, SON, HOLY SPIRIT)

1 Peter 1:2 - Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied. (FATHER, SON, HOLY SPIRIT)

because they "appropriated" most of their beliefs from other religions.