'Upasana' in Sanskrit literally means "Sitting near" but normally the term is used in Hinduism to denote a prescribed method for approaching a Deity or God or getting close to a deity/deities. In the Vedas, some Upasanas are prescribed whereby one meditates on the all-pervading Brahman as some aspect of creation, such as fire, water, directions, food, mind, joy, etc. Thus, Upasana can be described as a systematic practice of a prescribed method of worship for pleasing and winning the attention of the deity or it can be a deity-less practice of austerities involving meditating upon some aspect of nature as told in specific Vedic Upasanas. Normally such prescriptions of worship or meditational methods are taken from various Hindu scriptures, mainly the Puranas and Vedas. A devotee would consult the scriptures, or a person who knows them thoroughly, to get a prescribed form of worship (Upasana) for his/her deity of choice (Ishta Devata) and follow it faithfully to the best of his/her abilities.
Once the deity is pleased, She/He is said to grant the wishes of devotees either by directly appearing to the devotee and asking/granting what he or she wants, or reading the mind of the devotee and granting his or her wishes without making any appearance (unless one of the wishes is to see the deity personally.)
"The seeker of knowledge does not achieve his end merely by a study of scriptures. Without upasana there cannot be attainment for him, this is definite." -- Sri Ramana Leela, Ramana Gita I.22, quoted in Sri Krishna Bihkshu, Sri Ramana Leela (Pingali Surya Sundaram tr. 2004), p. 80.