If I understand your question correctly you are attempting to determine if a bacterial isolate(s) possess antimicrobial/bacterial activity. If so, may determine if the microbial inhibition you suspect is being produced by the organism of interest is a soluble factor or simply a more effective nutrient competitor by evaluating culture supernatants from your cultures serially diluted and added to fresh media which is inoculated with various microorganisms you suspect your antimicrobial agent is active against. I have attached a document that will provide you with tips and methods you may wish to try.
If the microbes are fungus then culture plate method can be used, in which you streak the plate with bacterial inoculate on the sides and fungal disc on the center. After incubation the growth pattern of the bacteria around the fungus can be examined to understand their relation.
I can suggest a crude test to start with and easy to do. Cross streak your test cultures on an agar plate with a perpendicular streak of the test strain, and later check for inhibition.
So for example you check 10 strains against one, then I would streak 10 cultures in parallel on plate, and the test strain perpendicular to them so that it crosses each line. If this strain inhibits anyone of them, you will see inhibition on plate.
And of course, the suggestions by Frank are also valid.
in case your organism is having an antimicrobial activity against bacteria, you can choose one representative each from Gram positive and Gram negative, say Bacillus and E.coli respectively. Perform a pour plate with preinoculated media having the representative bacteria. Allow it to set and after boring holes in the plate u can put the supernatant of the culture ( suspected to have antimicrobial activity) or can directly streak the said culture. After Incubation if you no zones of growth around the said culture, you can say that it has antimicrobial activity.... Normally supernatant is used when the antimicrobial compound is extracellular but if you donot know, streaking the said organism is the best option.
For clinical isolated bacterial antibacterial activity can check by gross streak method. Or you can use spot inoculation of isolated bacteria over the test organism seeded plate. Zone of inhibition around isolated bacterial spot indicates there is ability of isolated bacteria to kill test organism.
As i understood your question, you are asking about using antimicroibal activity of bacteria agaisnt other microbes. Well, I don"t know how other people are prioritising well diffusion method, but in my view, i think cylinder method is better; in involves growing bacteria on agar and then taking a cylindrical cut of this agar having bacteria and their toxins. This piece of agar can be placed on agar plate inoculated with bacteria, and read the results as antibiogram after growth period.