The basic model used when describing an enzyme and substrate complex is the 'lock and key' model. This is based around the notion that a substrate fits into the enzyme's binding region like a unique key fitting a lock, leading to the breakdown of the substrate into products.
More advanced models suggest that a number of substrates can bind with a number of enzymes by interacting with a number of catalytic regions in the enzyme. These catalytic regions are often comprised of specific amino acids which contain unique side chains (e.g. Tyrosine, which contains an aromatic ring), this allows certain types of substrates to bind with affinity to the enzyme.
Different bonds can be formed between the enzyme and substrate e.g. ionic bonds, disulphide bridges and Van Der Waal's forces. These facilitate the initial binding of the enzyme and substrate.