日本語を学び始めました！ "nihongo wo manabi hajimemashita!" 日本語＝”nihongo" = "Japanese" を＝ "o" = the particle that indicates a direct object (by the way I spelled it "wo" above and "o" here. It is technically "wo" but you practically never hear the "w" sound). 学び ="manabi" = "to learn" The verb here is "学ぶ" or "manabu" but it gets conjugated when it is combined with the second verb "hajimemashita" into "manabi." There is another word for learn also: narau 習う, which would change to narai in this usage. 始めました＝"hajimemashita" = "began" or "have begun". The verb is "始めます” or "hajimemasu" which means "to start something." In the past tense the "masu" is converted to "mashita".

｢日本語の勉強を始めました！｣ (にほんごの べんきょうを はじめました) is more natural. We seldom use the word 学ぶ in daily conversation.