It's not easy, is it, and the beginner preacher can get into some rather sticky situations.
Here's some thoughts:
1) It isn't easy and I don't think our task is necessarily to make it look easy to talk about the incarnation. The degree of unease and discomfort that people see can reinforce what we're talking about; people can see and hear that we are somewhat outranked by the truth that we're struggling to convey.
2) Be familiar with the classic systematic formulations. For example, the definition of Chalcedon really helps if you will think about it and master it, or rather allow what it expresses to master you:
We, then, following the holy Fathers, all with one consent, teach people to confess one and the same Son, our Lord Jesus Christ, the same perfect in Godhead and also perfect in manhood; truly God and truly man, of a reasonable soul and body; consubstantial with the Father according to the Godhead, and consubstantial with us according to the Manhood; in all things like unto us, without sin; begotten before all ages of the Father according to the Godhead, and in these latter days, for us and for our salvation, born of the Virgin Mary, the Mother of God, according to the Manhood; one and the same Christ, Son, Lord, only begotten, to be acknowledged in two natures, inconfusedly, unchangeably, indivisibly, inseparably; the distinction of natures being by no means taken away by the union, but rather the property of each nature being preserved, and concurring in one Person and one Subsistence , not parted or divided into two persons, but one and the same Son, and only begotten God , the Word, the Lord Jesus Christ; as the prophets from the beginning have declared concerning Him, and the Lord Jesus Christ Himself has taught us, and the Creed of the holy Fathers has handed down to us.
The vocabulary is a little challenging, but the basis of what they are saying is pretty clear:
One person, one soul, one body, just like us. But with two natures.
He is a real 100% human being, a man just like us but without sin.
He is also God, really 100% God, still being all that God is.
But there is just one "he", and it isn't like playing roles or transforming from one to the other and back.
There are no analogies because nothing else is like this.
Just like for the Trinity, there are no analogies because nothing else is like this.
We can find illustrations. For example I am Welsh and I live in Bordeaux. When I speak French you can tell there's something different about me, but you may not know what it is. From time to time, though, you can really tell that I am Welsh. But I'm always Welsh, whether you can see it or not, and my Welshness is not something I turn on and off. Usually. Anyway, as I said, there are no analogies, but sometimes we can find illustrations that may perhaps help a little.
3) Think about what he left behind when he became man. What did he leave behind, really?
4) Think about what he took on when he became man. What did he add in his humanity?
5) Think about words that we use. Some words can provoke a strong reaction. Don't necessarily avoid them, but be ready to explain what you mean and why you use that word.
for example, weak. It is clear that Jesus took on human weakness. What is weaker than a new-born infant? What is weaker than a thirsty man sat by a well with nothing with which to draw water? But ordinary, human, physical weakness does not necessarily imply moral weakness, weakness of character or weakness of judgement.
6) Remember that making a slip doesn't make you a false teacher. We learn from our slips and errors and struggle to try to find the right words to explain the inexpressible. False teachers deliberately try to gain a following for their novelties. It's different.
7) Don't get hamstrung by your own inability to fully understand. Luke records Paul saying "(ESV) care for the church of God, which he obtained with his own blood" while warning against false teachers. I know that among the elders listening to Paul there were probably none of the heresy-hunters that might take you on, so perhaps you do need to exercise care, but it would be a crying shame to fall short of preaching the wonder of the voluntary self-humiliation of the glorious Son of God because you are scared of accidentally tripping up.