It depends on your case. You can get data from different databases, but the ideal is acquire primary data from the companies across the supply chain.
LCA databases have relevant data and you can use factors to describe your case, but you can enrich the data (even the established data sets) if you collect them directly.
The question is where the data in the available databases come from ? These data are usually collected in the form of manufacturing data by the industries concerned as part of the environmental product declaration. Statistically averaged data on a larger number of firms is entered in the databases.
The ISO 14040 clearly explain how data should be selected. You should give priority to primary data.
Most of the data could come from direct measurements or industry interview, consultants. In alternative, you could use statistics and scientific literature. Finally, specific databases are available such Ecoinvent, ELCD, LCA commons.
Primary data - Through data collected/measured directly by company e.g. raw material, energy (electricity, NG etc.), wastes (emissions as well as solid waste) inputs for a particular process or product. Data maintained by process engineers, operators, EHS team would be required. Details to be followed as mentioned in ILCD handbook or ISO LCA guidelines as mentioned above by Petra Schneider and Pietro Goglio above.
Secondary Data - Through publications, open literature, softwares, LCA libraries etc.
OK, and if for instance my primary data measured by company is: 1 kg aluminium and 1 kWh electricity, how can I connect that with LCIA? It seems that I have to use than LCI Databases to find the appropriate processes for aluminium and electricity which is than considered as a secondary data. Or could you better explain? Thanks