You aren’t allowed to bathe your entire body (or even the majority of it) even if the water was heated up before Shabbos. This is a gezaira lest some people come to heat the water on Shabbos. (ShA 1 – MB 1, 2)
This gezaira applies even when you wash one limb at a time. However, you may wash just a couple of limbs (e.g. face, hands and feet) and stop. (ShA 1)
Water that is heated up on Shabbos cannot be used at all – even for washing wands. (MB 5)
A woman in the 7 clean days can wash required parts of her body with water heated before Shabbos. She should not use a cloth because of S’chitah. (MB 6)
If bathing the entire body will relieve a person in distress, it is mutar (in water heated before Shabbos only). This applies even if the person is not ill. (BeH “b’mayim”)
The Korban Nesanel holds that mikva is not included in the gezaira of bathing. You can rely on this in a pressing case. Otherwise you may only heat up the mikva to lukewarm. (MB 7 – ShaH 5)
Natural hot springs are not included in this gezaira. You are allowed to bathe in them as long as you do not remove the water from the ground and put them into a tub. (ShA 1 – MB 8)
If the hot springs are used only for therapeutic reasons, it is ossur because of Refuah. (MB 8)
Bathing your entire body in cold water was not included in gezairas rechitza. However there is a well established minhag not to submerge even in cold water lest you come to wring out your hair. It seems from the Mishna Berura that showering in cold water is not included in this minhag. (ShA 1 – MB 9, 18, 21)
It is considered bathing in hot water to shower first in cold water and then to stand near a fire (or oven wall) and allow the fire to warm the water upon you. Some hold that this is likewise forbidden with your hands (even with one limb). Therefore you must dry your hands well before warming them near a fire. (ShA 4, 4 – MB 17)
Never put a bowl of hot (yad soleddes) water on your belly – it’s dangerous and on Shabbos it could spill and become Rechitza. (ShA 6 – MB 19 – BeH “shep’omim”)
There is a machlokes Rashi and Tosfos regarding the use of a sealed hot water bottle to relieve a sore stomach. Tosfos hold its ossur because of Refua. You can be maykil if you really need to. (MB 19)
The minhag is not to submerge in a river or pool of water on Shabbos because of the concern of wringing out hair. (MB 21)
When washing your hands and face in a river, be sure not to carry the water on your hands. Be sure to dry them before walking 4 amos. (MB 21)
If you are walking in reshus horabim and rain is drenching you and your clothes, you are allowed to continue while “carrying” the water. The Chazal did not decree in cases where it is impossible to avoid transgression. (MB 23)
A woman is permitted to purify herself in a mikva on Shabbos. However since the minhag is to not submerge in pools on Shabbos, it appears as Tikkun – that you are dunking solely for purification from tuma. Therefore only go to the mikva on time. But if you have postponed mikva already, postpone it further until after Shabbos. (ShA 8 – MB 24)
Is a man allowed to go to the mikva for keri on Shabbos? Some poskim claim that it appears like tikkun. Most achronim are maykil since it does not really fix a man these days. Because there is no prohibition for a baal keri to daaven and learn Torah these days. Certainly if one became a baal keri on Shabbos or Yom Tov itself one does not need to be machmir. Remember to avoid wringing out your hair! (MB 24)
You are allowed to wash places on the body that have hair – like a bearded face and a head of hair. Just do not wring out your hair. (ShA 9 – MB 25)
Animal fat-based soap is okay to use during the week. The Gr”a held that smearing the soap is like drinking it which is not kosher. If you have a non-fat based soap readily available, it is best to be concerned for the Gr”a. (BeH “Bish’ar”)
Warn people that today's bar soap is ossur to use on Shabbos. It’s an av melacha of M’machayk. (MB 30)
You aren’t allowed to go into a bathhouse on Shabbos just to sweat in the steam. If you are there for other reasons, the Rama still forbids it. Accordingly, getting dressed inside a steaming mikva room must be done quickly. If it’s impossible to avoid sweating, don't go. Women can rely on the Mechaber if they don't have kavana for sweating. (ShA 12 – MB 35, 36)