Adjacent nucleotides are held together by phosphodiester bonds - these are covalent bonds formed between the 5' phosphate group of one nucleotide and the 3' OH group of another. This way the backbone is phosphate-sugar-phosphate-sugar-phosphate...
The nucleotides on the two strands are held together by weak hydrogen bonds. A with T (2 weak H bonds), G with C (3 weak H bonds).
