I would take a dna sample of good quality (od260/280 of 1.7 -2.0) and run an annealing temperature gradient (if your lab has a gradient pcr machine) of Tmminus5 to Tm plus 5 degrees centigrade. Low temperatures will give many bands and a few temperatures will give clean product and top temperatures may fail.. If your amplimer is less than 1000 bases then extension time of 30 seconds is plent with an annealing time of 10 seconds and a denaturation time of 30 seconds. Start with 35 cycles of pcr and about 30,000 copies of your target dna template.
Amount of primer is approximately 0.5 uM oligo in the PCR reaction
Most changes in pcr conditions result in too many unspecific bands ( low temperatures.too much salt/dna/enzyme) or failed pcr (too high temperatures/too little dna)
The mentioned publication discussed the possibility to get shorter-time PCR reaction and states in its background the following:
"Current standard methods include near universal denaturation temperatures and times of 95 °C and 15–30 s, respectively, annealing/ polymerisation times of 15 s–1 min and optional separate polymerisation times of 45 s–2 min".
"that it is possible to use significantly modified protocols to achieve faster PCR results without compromising the sensitivity or specificity of the PCR assay. Although the extension rates of native Taq polymerases ranged from 10 to 45 nucleotides/second, some polymerases achieved up to 155 nucleotides/second".
1) To optimize the Annealing Temparature: From your primer sequences you'll get their melting temparature i.e Tm. Suppose the Tm for forward primer is (Tm)f and the same for reverse primer is (Tm)r. For a good primer pair the maximum difference between both the Tm should be 4.
So, let the (Tm)f > (Tm)r
Now to calculate the annealing temperature of the primer set, we will start from the temperature of (Tm)r-5 and then with the same master-mix, template and primer-set, we should set a gradient PCR with separate annealing temperatures and they will be like (Tm)r-3, (Tm)r-5, (Tm)r-7, (Tm)r-9, (Tm)r-11, and so on. Hopefully between these said range you'll get your PCR-amplicon and at which temperature you'll get the most intensified PCR-amplicon with no non-specific amplification should be your desired Annealing temperature (TA) for those primer-set.
2)Primer concentration: It should be 10-20picomoler/microliter or 10-20micromoler.
3)Extension time: Extension time will depend on the polymerase type and the product length (amplicon size).
For 300-400bp the extension time 40secs will be enough, for 500bp and more you can set the extension time ~1min (but for high fidelity enzyme it should be for ~1.5-2mins).