Assuming you've sorted and indexed your bam file with "samtools sort" and samtools index", you can pull out reads from a given region as follows (for example from chr1:1000000-2000000)

samtools view <BAM> chr1:1000000-2000000 | wc -l

Now, if you also want to limit on mapping quality, use the -q option (here I am asking for MAPQ >= 10).

samtools view -q 10 <BAM> chr1:1000000-2000000 | wc -l

If you need to look for reads overlapping many regions, use BEDTools.

intersectBed -abam <BAM> -b regions.bed > reads.in.regions.bam