LITTLE BOXES= A metaphorical way of referring to little houses.

THE HILLSIDE= The side or slope of a hill, situated between the foot and the summit.
The author of the song may be thinking of a city in particular or maybe she chose “hillside” just randomly, but there is a strong psychological factor to make an American person think of the suburbs as an area on the hillside. In England, the city centre is called “city centre”, but in America the city centre is called “downtown”. That name evokes the idea of a city which is funnel-shaped (see funnel), so if the centre is down, at the bottom of it, then the image for the rest of the city is up the hill; the suburbs, being on the outskirts, on the edge of the city, must be on the hillside too, going up, just to make the unconscious downtown image valid.

TICKY-TACKY= 1) Building material of poor quality. 2) Marked by a mediocre uniformity of appearance or style.
The meaning intended here is most probably 2, but of course, as it often happens when a word has more than one meaning, the meaning 1 also rings in your mind when you hear the song, so both meanings have an impact.

THEY CAME OUT ALL THE SAME= In the university, they all suffered the same influences and changes and when they finished they were all identical (same way of life, same way of thinking, same behaviour, same likes...). Here is a criticism of the supposed uniformity of American middle-class society. Of course, people from many countries in the world would be shocked at the thought of considering American middle class as something uniform, but everything is relative and the author certainly did (probably because they were all very different from herself, so distance unifies features).

THE GOLF COURSE= The green field with holes and sand pits where people play golf.

DRINK THEIR MARTINIS DRY= Here, “dry” functions an adverb (-how do they drink their martinis? – dry), but it is actually an adjective (-what kind of martini do they drink? –dry martini).
A “martini” can be either of two things:
1- An Italian brand of vermouth (a kind of wine with herbs) which comes in two main varieties: sweet and dry. A dry martini is more bitter, less sweet, than a sweet martini. Since the most popular vermouth is Martini & Rossi, people often use the word “martini” for any kind of vermouth, especially in Europe.
2- A popular cocktail made with vermouth and gin. A dry martini is a cocktail with less vermouth than usual (and so, more gin).
Since this is an American song talking about clichés, when they say “a dry martini” they most probably mean number 2 here.

SUMMER CAMP= A place, usually in the countryside or in a forest, where children go to have fun in the summer. They usually live in wooden cabins or tents and have lots of outdoor activities and games, supervised by counsellors.

RAISE A FAMILY= If you raise a family, you marry, have children and bring them up (and also educate them, but that’s optional). If you raise an animal you have an animal and feed it so it grows up (probably to sell it or eat it or get derivative products such as milk or eggs).