Robert Burns manages quite a bit of technique in this short little poem! To start, he uses the stock simile of a rose to represent love. Roses are special and beautiful, just as true love it. He states that the rose is "newly sprung in June." This is using the year of life metaphor to suggest the newness of the love as it appears in the newest part of the year which was born/reborn in spring and shows some young maturity in June. He then uses another simile to compare his love to song that is "sweetly played in tune." That is a very pleasant sound image, as opposed to sound that would be described as harsh or discordant.
In the next two stanzas he explains that he will love his dear one until "the seas gang dry," until "the rocks melt wi' the sun" and until "the sands o' life shall run." These kinds of hyperbole, or overstatements are typical in love poetry. He can't literally love her that long, but he only means that he will love her forever.
In the final stanza he is bidding her farewell which then seems to be the purpose of the poem. He is assuring his true love how much he loves her even though they will be parted for some time. He again uses hyperbole to say that they will be united again, even though a seemingly insurmountable number of miles may separate them.
The poem also uses a predominate iambic meter with alternating lines of tetrameter and trimeter. This means that the predominate meter is unstressed syllable / stressed syllable with that pattern occurring 4 times in the first and 3rd lines and that pattern occurring 3 times in the 2nd and 4th lines. The short lines emphasize the sing-songy quality of the poem and the abcb rhyme scheme also enhanses that.