Check before the box is unpacked
Note the condition of the outer packaging, whether any cold chain material was still cold on arrival, and the date and time it was received. A shipment that spent a weekend in a warm depot is a different shipment from the one that was dispatched, and the only evidence of that is what you record now.
Photographs cost nothing and settle arguments that would otherwise come down to memory.
Record the identifiers, not the impression
For each item write down the compound as printed, the quantity per vial, the number of vials, and the lot number exactly as it appears on the label. Copy the string rather than paraphrasing it.
If the label carries no lot, record that fact explicitly. An absent identifier is itself a finding, and a blank field six months later is indistinguishable from a field nobody filled in.
Tie the paperwork to the material
File the certificate against the lot number rather than the order number or the compound name. Orders get split and compounds get reordered, but a lot is unique.
The test of a good record is simple. Pick up any vial at random and see whether you can reach its certificate, its arrival date and its storage history without asking anyone.