The addition of a new base to an oligo takes place in four steps:
1) The trityl group is removed from the 5' oxygen
2) The two bases are coupled together
3) The phosphate is oxidized, stabilizing the bond between the two bases
4) Any oligos which did not participate in the coupling reaction are capped (to block addition of subsequent bases).
The difference between the synthesis of a normal oligo with a full phosphodiester backbone and a oligo with a partial or full phophorothioate backbone is the choice of oxidizing agent used in step 3. A phophodiester bond is produced by using iodine and water to add a fourth oxygen to the phosphate. A phosphorothioate bond is produced by using Beaucage reagent to add a sulfer to the phosphate. Once either the sulfer or the oxygen has been attached to the phosphate, the bond is stabilized and will not be affected by the subsequent cycles of chemistry. By switching back and forth between the two oxidizing agents, a chimeric backbone can be constructed.
Please see our technical bulletin on The Chemistry of Oligonucleotide Synthesis (chemical-synthesis-of-oligonucleotides.pdf) for more details on how oligos are synthesized.