two -OH [hydroxyl] groups combining with a molecule of H2O being shed, leaving -O- between the two monomers that join up e.g. a number of reactions between respective pairs of glucose molecules to form the polymer called a polysaccharide
an -NH2 [amino] group of one amino acid reacting with a -COOH [carboxyl group] of another a. a. to form a peptide bond [essentially a special type of amide formation [-CONH group], once again by condensation i.e. the extrusion of one H2O molecule. When several a.a.-s join up you get a polypeptide, if just a few join up you get an oligopeptide.
The opposite occurs in hydrolysis i.e. breakage of a bond between monomers using H2O [some drugs are metabolized by hydrolysis in the liver using one of the cytochrome c [CYP] enzymes [others by suphation, oxidation, etc. [oc not a breakdown of a polymer here, although digestion in the gastrointestinal tract often involves hydrolysis reactions involving breakdown of polymers]].
Hope this helps.
If you are hot on chemistry, young man, you can add to my answer with details of non-biological examples like polyethylene, polypropylene, polyurethane - go on, I am sure OP will be delighted!
Polyethylene and polypropylene would be addition polymers. They are formed when the carbon to carbon double bond opens up and links the to the next chain. So in the polyethylene in one of its constituent molecule (2 carbon atom chain containing a double bonds) the double bonds open up and link to the neighbouring ethylene molecule and form a chain of many ethylene molecules. For polypropylene the double bond in the propylene molecule (3 carbon chain with 1 carbon to carbon double bond) would open up and link to form an addition polymer - polypropylene. As for polyurethane, I don't know what the **** that is 😂