The most straightforward way is using CrossMap.

Taking from hg19 to hg38 as example:

pip install CrossMap

CrossMap.py bam -a hg19ToHg38.over.chain input.bam output
#.bam extension will be added automatically

genome liftover chain files can be downloaded here: http://hgdownload.cse.ucsc.edu/goldenpath/hg19/liftOver/ (change according to your needs)

It is suggested to always use ‘-a’ option according to the CrossMap website.

Source:
http://crossmap.sourceforge.net/#convert-bam-cram-sam-format-files