Go to http://www.mirbase.org/search.shtml
Under Single sequence searches: paste your sequence of interest
Select whether you want the search for stem-loop sequences (intact precursor sequence) or for the shorter sequences of mature miRNAs.
Select the type of the search BLASTN or SSEARCH. Choose BLASTN to search for a miRNA in a longer sequence. SSEARCH on the other hand is useful e.g. if you have a short sequence motif that you want to find in the library of miRNAs.
Select the Maximum number of hits to display and species of interest.
The limitation of the search is that it supports sequences up to 1000bp, so for example 3'UTRs longer than 1000bp could not be searched at once.