FastQC is one of the most popular quality control tools for high-throughput sequence data.
To get a FastQC report for your FASTQ files, run the public FastQC analysis workflow. The workflow outputs a report file whose name ends fastqc.b64html that can be viewed directly in your internet browser.
The left sidebar of the FastQC report shows its contents. For a full explanation of the information shown in the report, we refer you to the package tutorial, in particular to section 3 on Analysis Modules.