For an introduction on what gensim does (or does not do), go to the introduction.
To download and install gensim, consult the install page.
For examples on how to use it, try the tutorials.
>>> from gensim import corpora, models, similarities
>>>
>>> # load corpus iterator from a Matrix Market file on disk
>>> corpus = corpora.MmCorpus('/path/to/corpus.mm')
>>>
>>> # initialize a transformation (Latent Semantic Indexing with twenty latent dimensions)
>>> lsi = models.LsiModel(corpus, numTopics = 20)
>>>
>>> # convert the same corpus to latent space and index it
>>> index = similarities.MatrixSimilarity(lsi[corpus])
>>>
>>> # perform similarity query of another vector in LSI space against the whole corpus
>>> sims = index[query]