Hi, Raymond. I don't know your specific situation, but I'll offer some...observations; almost said "quick observations," but I can't even do grocery lists in 100 words. And these are worth every penny you just paid for them. :-)
1) Documentation, documentation, documentation. As Philip noted, it all starts with traditional genealogical documentation. I've spoken with people who disagree with that statement when it comes to researching an adoption or NPE, but it's still the cornerstone. For example, detailed information about the timeframe, geography, and other extant family members near that time and place may end up providing the deductive clue needed to put the DNA data to use.
2) Evidence is evidence. DNA testing (whether yDNA, autosomal, or mitochondrial) should be treated as any other form of evidence. By itself, the only story it can tell is anthropological in nature: potential ethnic compilation or ancestral diaspora measured in thousands of years. You need a paper trail to which the DNA results can be applied as evidence, as substantiation of the story of your lineage.
3) One edge of the Ahnentafel. Dealing with yDNA and myDNA is more binary--more "yes" or "no"--than with the fascinating complexity of atDNA. The good news is the Y-chromosome is going to run along the bottom edge of the left side of your Ahnentafel fan chart; any yDNA match is going to connect only through there. Keeps the hunt very focused. But you still may need solid documentation on the rest of your pedigree to confirm the Most Recent Common Ancestor.
4) Mutation...no, not like the X-Men. With yDNA and mtDNA, the genetic material doesn't recombine, so any variance from generation to generation occurs as the result of mutation, not recombination. As time progressed from the sequencing of the genome, markers--specific areas/locations on the chromosome--were identified and studied; for yDNA, that means we have a better handle today than ever before about the probability any given short tandem repeat (STR) will mutate from one generation to the next. So with yDNA, the testing companies can give you an estimate of generations to MRCA, but not possible cousin relationship as with atDNA.
5) The genealogical timeframe. Because yDNA and mtDNA markers mutate at a positively glacial pace compared to atDNA recombination and dilution--which results in less than a 50% chance that a match with a confirmed 4th cousin will even be detected--you are quite likely to have an exact or 1 to 2 GD (genetic distance) with your 5th or 6th great-grandfather. And the fact that you're alive today means you had a direct-line paternal ancestor alive back in the Bronze Age...even about 120,000 years ago in the Great Rift Valley of Africa. But we're pretty much reliant on the surname-era for evidenciary verification of genealogy. That brings us to...
6) Number of markers and specificity. Generally speaking, the more markers tested, the merrier. When I first tested with FTDNA, you could buy 12-marker and 25-marker panels. They scrapped those less determinate tests and start now at 37 markers. But if you have a common haplotype--for example, similar to the Western Atlantic Modal Haplotype (the most common in Western Europe)--you may still have a ton of assigned matches at 37 markers. My recommendation would be to prioritize only those with a GD of 0 and 1, in that order; consider a GD of 2 and 3 only if the others dry up; and don't worry about GDs of 4 or more. At that point, it's getting to be highly unlikely you share an ancestor more recent than six or seven generations, but you may well be related as recently as 15 generations. At 67 markers tested, revise those GD estimates up by one: prioritize GDs 0 through 2; drop to 3-4 as a last resort; and don't worry about 5 or higher.
7) Spread the wealth. If you tested with FTDNA, post at least a basic paternal-line GEDCOM for people to reference. Baffles me why so many don't do this. Also make your results available on Ysearch. The more opportunity folks have of finding a possible connection, the better. And if someone reaches out to you about a match, respond promptly. Doesn't mean it has to be an authoritative response, just a prompt one. Open up the line of communication. Otherwise, the person who tried to contact you will likely just move on to the next on the list.
8) Surname yDNA projects. Two words: can't hurt. When I was first tested 13 years ago I had the great fortune to fall into a busy surname project (very common surname) with an active, attentive, thorough project manager. When FTDNA released results, he would pour over them, match us into groups by marker consistency and least GD (not just by haplogroup which seems more common, and automated, today), and once enough members were sorted into a group, publish a reference, benchmark haplotype for that group. I haven't seen a great deal of benefit to surname projects in recent years but, an important caveat, I've looked only at a handful; no doubt there are great ones.
9) SNPs and haplogroups. Unlikely to prove of any genealogical value. You'll get a predicted yDNA haplogroup based on your STR results, but the only way to confirm yourself on the haplogroup tree is through separate testing of SNP (single nucleotide polymorphism) markers. If you find it interesting, which I do, go for it. But there's nothing SNPs can tell you in the genealogical timeframe that STRs can't.
10) Research planning and triangulation. Last, depending on your situation, a tactical plan for testing additional individuals may be in order. The term "triangulation" applied to genetic genealogy came into being before the advent of atDNA testing, so has a different connotation there. But for yDNA it essentially means broadening your base, like a pyramid, by identifying others to test. With atDNA, a good rule of thumb is to test a lot of close family members: both parents, some siblings, some aunts and uncles, some 1st and maybe 2nd cousins. That's a waste of money for yDNA unless investigating adoption or NPE. While a single-step mutation on a fast-moving marker can occur at any generation, the odds are extremely high that your yDNA is an exact match to your father's and your grandfather's...and very likely to you g-grandfather. The better approach is to start with a clearly stated hypothesis, and plan a sequence of tests accordingly. From personal example: family history said that our paternal lines stemmed from an unknown man who had four male children in the Carolinas in the late 18th century. There was secondary and anecdotal evidence supporting this, but insufficient to meet the genealogical proof standard. Over the course of a year, we identified living males who had adequate documentation to show that they descended from each of these four men. DNA testing positively confirmed the hypothesis, linked a lot of cousins, and further identified another branch of the family that did not descend from the father of the four brothers, but likely from one to two generations earlier. Progression of research that would have been simply impossible without yDNA testing.