Many people today have in their home non-electrical apparatuses for preparing seltzer. One fills a bottle with water from the tap, and then attaches it to the spout on the machine. He then presses a button that thrusts carbon dioxide into the water to make it carbonated. A cartridge situated in the back of the machine allows one to prepare approximately 60 liters or so of seltzer.
Rav Yehoshua Neubert (contemporary), in his Shemirat Shabbat Ke’hilchatah (vol. 1, p. 114), writes that it is entirely permissible to use such an apparatus on Shabbat for making seltzer. There is no prohibition whatsoever involved in injecting carbon dioxide into water to make seltzer, as long as no electricity is used. And attaching the bottle to the apparatus does not constitute "Boneh" ("building"), because it attaches and detaches very easily without requiring any special effort or tools.
It should be noted, however, that one is allowed to make seltzer only if it is needed on Shabbat itself. One may not prepare seltzer if it is needed only after Shabbat, as it is forbidden to prepare on Shabbat for after Shabbat.
Summary: It is permissible to make seltzer on Shabbat, provided that no electricity is involved (and seltzer machines generally do not involve electricity), and that the seltzer is needed on Shabbat.