As a matter of fact... :)
My recommended methodology has changed slightly for situations where you do not know the adapter sequence. It still requires paired reads, though. First, you can determine the adapter sequences like this:
bbmerge.sh in1=read1.fq in2=read2.fq outa=adapters.fa reads=1m
(for small RNAs, add the flags mininsert=15 mininsert0=15)
Then you can run BBDuk:
bbduk.sh in1=read1.fq in2=read2.fq out1=trimmed1.fq out2=trimmed2.fq ref=adapters.fa k=23 mink=11 hdist=1 tbo tpe
This is more sensitive than just running BBDuk with the tbo flag and no adapter sequence.
In fastqc output you get over represented seqences, but they get it from first 200K sequences which is nothing in comparison to library size.
but you can make a consensus of overrepresented sequences and then check by
keep on editing the sequence unless you get output of 90000-99000
I am sure there is an another way, which is with alignment something, I had read in a paper where authors took bulk of ClIP-seq data and then trimmed their adapter by some calculations.
Here is the paper, see in their method section they did something to remove adapters