the question is a bit general, I would recommend you to keep the substrate and temperature stable to develop the desired communities you re interested in and try monitor the communities either via SEMicroscopy, maybe FISH or qPCR. If you re only interested in the sludge then check for the SVI and settleability. For online continuous measurements I would initially try measure pH and redox, these two can say a few things for the status of your sludge.
Many answers here are relevant. But if you mean you want to isolate them, then culturing on agar plate would help as well. After the culturing are done, then you may isolate them and send for 16S RNA sequencing. But of course using DGGE, PCR, or FISH will be more efficient.
For mix culture: The easiest way is feeding the constant COD (such as 1g/L) in a batch. Feed composition should be constant also. And you can measure pH, redox, SS, and COD after a period of time (12h, 24h). COD in the effluent should be stable. If your sludge is anaerobic, you can also measure biogas production per day.
Acclimatize your bacterial culture. Below is a brief idea of what I had done when I did my dissertation:
1. In a 3L glass beaker, add 300 ml wastewater from aeration tank and 2700 ml fresh water on day 1. Wastewater should be collected from mid depth aeration tank where you can see a good mixing. Add your bacterial culture to this mixture and aerate the beaker with any aeration method.
2. Day 2, stop the aeration and allow the sludge to settle. Drain the supernatant. Add 600 ml of wastewater from aeration tank and 2400 ml of fresh water. Start aeration.
3. Repeat the process for 10 days till it is 3000ml of wastewater from aeration tank and 0ml fresh water.
Monitor daily for temperature, DO and pH. Also carry out microscopic examination to see the activity of microbes. Presence of nematodes indicate good quality treatment. Check SVI to have better idea of it.
Once acclimatized, you can vary the rate of aeration to see the minimal requirements of your bacterial culture.
Regardless of the medium used, you will only cover probably >1% of the bacteria. So use molecular techniques. Now with amplicon sequencing (using NGS DNA protocols) of the 16S rRNA genes, you can fingerprint your community at a deep level, and so follow changes over time
It is critical that you monitor the pH value of pH-value of the sludge as high acidity (pH of 5 of less) or high alkalinity (pH of 8 or higher) could adversely impact the bacteria.