Sento vs onsen
A sento is a public bathhouse using regular heated tap water, found in ordinary neighbourhoods rather than hot spring regions; an onsen, by contrast, draws on naturally occurring geothermal hot spring water and is more associated with dedicated resort towns. Osaka, as a dense city rather than a hot spring destination, is a sento city first.
How a visit works
Sento are gender-separated, and the etiquette is consistent everywhere: wash and rinse thoroughly at the individual washing stations before entering the shared soaking tub, keep long hair tied up and out of the water, and don't bring a towel into the bath itself. Bathing is done without swimwear, which is standard practice and not treated as remarkable by anyone else there.
Tattoos
Many sento and onsen historically restrict visible tattoos, a legacy of their association with organised crime in Japan, though policies vary a lot by establishment and are gradually loosening, especially at bathhouses used to a more international clientele. If this applies to you, it's worth checking a specific venue's policy, or looking for tattoo-friendly options, before turning up.