Pol III is unusual (compared to Pol II) by requiring no control sequences upstream of the gene, instead normally relying on internal control sequences - sequences within the transcribed section of the gene (although upstream sequences are occasionally seen, e.g. U6 snRNA gene has an upstream TATA box as seen in Pol II Promoters).
There are three classes of Pol III initiation, corresponding to 5S rRNA, tRNA, and U6 snRNA initiation. In all cases, the process starts with transcription factors binding to control sequences and ends with TFIIIB (Transcription Factor for polymerase III B) being recruited to the complex and assembling Pol III. TFIIIB consists of three subunits: TATA binding protein (TBP), a TFIIB-related factor (BRF1, or BRF2 for transcription of a subset of Pol III-transcribed genes in vertebrates), and a B-double-prime (BDP1) unit. The overall architecture bears similarities to that of Pol II.