Part 1 : how to detect mutations
The keywords you are searching for are "variant calling". Basically you have to map sequencing reads to a reference genome (or gene) and then estimate for each position of the genome if the observed difference of mapped reads and the reference is more likely a sequencing error or a mutation (in genomic glossary - variant).
Popular tools for variant calling are GATK, FreeBayes or bcftools (previously part as Samtools package).
The question you linked asks for quick alternatives to simply looking for variants. Indeed, you can just visualise the mapped reads to the reference sequence and see if the variant is there or not. CIGAR is just a notation of read alignment used in sam files (files with mapped reads), you can find good explanation of CIGAR strings here.
The follow-up about "How to estimate an effect of mutation" is in @DevonRyan 's awesome answer.