You should really read about both these file formats. As swbarnes mentioned, FASTQ and GTF hold different kind of information. GTF stores the annotation of a reference sequence. For example a GTF for a genome sequence will have the information about the locations of features such as genes, transcripts, exons, start codon etc.
FASTQ stores the sequence of a read obtained from sequencing along with the quality scores corresponding to each position.
As mentioned by others, asking for interconversion of these file formats, makes no sense.
I guess what you are asking for is "How to obtain novel annotations with a FASTQ file at hand?
This also depends on what you want to annotate.
The sixth column in a GTF file refers to a score; you can assign expression values to different features. You can calculate expression using the read counts. If these are RNAseq reads then expression can be measured using packages like tophat-cufflinks, RNAstar or some others.
If you are doing ChIP-Seq then you can generate a GTF with a new feature called TFBS (transcription factor binding site) and annotate the locations. A popular package used for ChIP-Seq analysis is MACS, which takes your reads and outputs the TFBS in the form of a BED file which also stores co-ordinates. You can convert BED to GTF. You can also assign scores based on the read counts at different TFBS.
If you do not have a reference genome or if the annotation of the reference genome is incomplete, then you should first assemble your reads. If you have a reference genome then you can go for a reference guided assembly of the transcripts to obtain novel transcripts or splice variants; Cufflinks does this.
If you do not have a reference genome then you should go for de-novo assembly of your transcriptome and annotate the transcriptome for start codons or other features of processed transcripts. Velvet and Trinity are popular packages that do de-novo assembly.