How can sequence analysis establish whether a genomic sequence is a functional gene or a pseudogene?
There is no good single answer genes which long have been though to be pseudogenes may have function in a very narrow set of cells.

That being said, some of the best indicators are; destruction of the ORF, accumulation of C->T and G->A mutations (methylation/deamination in mammals).

Expression is probably not a good indicator, because once you start including long non-coding RNA, pseudogenes may be transcribed, but may not have a protein-encoding function (if any).

You can also measure loss of introns and a poly-A tail in the DNA sequence which is consistent with a retro-pseudogene, but that doesn't mean that the 'pseudogene' doesn't have it's own function.

Overall, evolutionary conservation is the fastest and most reliable indicator, but ultimately genetic knock-out would be required.

If you have more information about the pseudogene, there may be other useful information which could help distinguish the two.