Many combine Christianity and Buddhism in different ways these days, and it is interesting to explore some of the ways this happens.
It is of course possible to combine the two in a superficial way, without looking too much at the clashes between the philosophy of Buddhism and the mainstream theology of Christianity. But if we take it more seriously, we need at some point to reconcile the two in a more thorough way, and this usually happens through giving priority to one or the other.
We can give priority to the mainstream theology of Christianity, with its assumptions of the reality of a separate self and soul, and use whatever is useful in Buddhism within this context. Often, this means using some of the Buddhist practices for clarity of mind or for opening the heart.
We can give priority to Buddhism, with its emphasis on the inherent absence of a separate self anywhere, and use Christianity within this context. For instance, we can use Christian forms of prayer and meditation emphasizing the heart and embodiment. (In my own experience, the quality of heart awakening through Christian practices have a flavor quite distinct from that of Buddhism.)
Or we can give priority to the mystic’s view of Christianity, which already is pretty much aligned with the philosophy of Buddhism. Some Christian mystics describe oneness, a separate self one with God and all there is, but there are certainly many others who describe realized selflessness, as in Buddhism. In this case, there is a nice alignment of the philosophy and descriptions in both traditions, and we are free to use practices from both as well.