。
I would like to express my gratitude to everyone who has helped me.
Literal
Care-received all [possessive-の] people [to-に] gratitude [possessive-の] words [object-を] want-to-state [quotative-と] think.
Classic formal expression. お世話になった is a ubiquitous set phrase meaning 'who looked after me / who helped me.' 方々 is the respectful plural of 人. 述べたいと思います is the standard formal pattern for expressing a wish — [verb-たい]と思います softens direct desire into a polished announcement. The kind of sentence you hear at ceremonies and formal speeches.