Let's talk about one of the most common combinations - adjective and noun and their agreement. To agree means to choose a correct form of an adjective (gender, number and case) because according to rules, adjective depends on a noun. A noun in this combination is a main word and adjective is subordinate one.
Let's take for example the sentence: "Я никогда не читал настолько (интересный) книг" (I have never read such (interesting) books). Our task is to agree the adjective "интересный" with the noun "книг".
To agree them correctly, you should determine noun's gender, number and case. We know that the noun "книга" (a book) is feminine and when we look at its zero ending, we understand that it is used in plural form, genitive case. Then we should write the adjective in the same form. The feminine gender of "интересный" is -> "интересная"; plural form of "интересная" -> "интересные"; genitive case of "интересные" - "интересных".
Then we get the expression: "Я никогда не читал настолько интересных книг".
In dictionaries and tasks the words are presented in singular form. Short adjectives also agree with nouns in gender, number and case, however, such expressions are set expressions and used in speech as idioms.
На босу ногу - without one's stockings or socks on. ("боса" - the short form of "босая").
Try to do some simple exercises on agreement.
Зимн() лес - a winter forest Тёмн() небо - a dark sky Сладк() мороженое - sweet ice-cream Хорош() погода - a nice weather Лучш() другу - to a best friend С младш() сестрой - with a little sister Красив() цветы - beautiful flowers Без черн() хлеба - without brown bread Мелк() дождь - light drizzle В нарядн() платье - in a gala dress Нов() работой - by a new work Золот() руки - gifted hands