See also Language & Tone
Consider whether it is necessary to mention a person’s age. Is the modifier in the phrase ‘the old man who sits out the front’ relevant to the context or not? In some cultures ‘old’ can imply wisdom and in others weakness and senility, and ‘young’ can likewise be a veiled reference to health or inexperience.
Older people is acceptable as a comparative; elderly people is also acceptable; never use ‘the elderly’ or ‘the old’.
Use pensioners only if it is relevant to the context: does the reader need to know they are collecting a pension or do you just mean ‘retired’? Never use the term ‘old-age pensioner’. ‘Senior citizen’ is OK to use, though can seem like a patronising euphemism in some contexts. Note that ‘pensioner’ may have a different meaning and different connotations in different countries. For example, in some countries all former government employees receive a pension, irrespective of age.
Young is OK to use but take care to avoid giving unintentional offence by implying inexperience; never use ‘the young’.