Phred Quality Scores. Q=-10 log(10)P, where P is the chance of the nucleotide being wrongly identified. They are coded as a string of characters from ! to ~ in ASCII code ordering (this means scores go from 33 to 126, but really scores never exceed 40). Scoring encodings vary depending on the platform (Illumina or other) and the software version.
Sequence of steps
Demultiplex. Split the sequences and asign them back to their original samples based on their "barcodes"
Remove barcodes. Clip/Trim edges of sequences
Analyze Quality
Quality Analyses. An example with FASTQC (good: http://www.bioinformatics.babraham.ac.uk/projects/fastqc/good_sequence_short_fastqc.html#M0 vs bad: http://www.bioinformatics.babraham.ac.uk/projects/fastqc/bad_sequence_fastqc.html#M0)
Per base (nucleotide) qualities. It is normal to drop as one moves on to the end of the read
Per sequence (average) quality scores. Should have a distinct peak at a high value (>35)
Per base sequence content. Allows you to see over-representation of specific nucleotides at specific positions, a mark e.g. of incorrect trimming
GC content of sequences (as compared to the expected for the genome)
Other less noteworthy biases such as k-mer contents and adapters (provided you 've done trimming correctly).