Assuming you took a copy of the whole data directory including
base, etc, then you can simply ensure that PostgreSQL 9.3 is installed and:
postgres -D /path/to/data/directory -c "port=5433"
then in another terminal use
pg_dump to dump the database(s) from the database running on port 5433 with (eg)
pg_dump "dbname=mydb port=5433".
This process is well-covered elsewhere; it's just starting a new PostgreSQL server and dumping the database. So I won't go into detail and cover all the possible errors, etc.
However, if you only copied the
base directory, you're pretty much stuffed. The data is sort-of there, but it's missing all the vital information that tells the system what databases there are, handles crash-safe updates, keeps track of rolled back vs committed transactions, and lots more.
If you only have
base, recovery might be possible but would probably involve paying an expert for a fair bit of time to try to extract the data. Even then, it'd likely be significantly corrupted - duplicates in primary key columns, deleted data reappearing, old versions of updated rows reappearing, recently committed transactions only half-complete, etc.
So I hope you kept backups.