If you have a UN document symbol (e.g., E/CN.15/2010/L.16), you can often find the document by searching the web using that document symbol. Finding older and more obscure documents, however, may require more work. To search UN documents by keywords, there are two main options: the full-text database ODS; and the UN documents index UNBISnet.
ODS has full-text documents, but only from about 1993-present. Older documents are being added. Unfortunately, ODS doesn't always capture documents produced by UN organs. (Other indexes and databases of UN documents have the same problem.) ODS allows keyword searching and other search options.
UNBISnet has coverage of older documents than ODS does; coverage begins in about 1979. Links to full-text documents are often provided, but if they are not, try searching for the document on the web or in ODS.
Both of these sources have UN resolutions back to 1946.