How do I group similar type of skills together?
If all you have is the name/word, then I see only two ways:


You can look at word similarity, basically by measuring how similar the spelling is. There are a number of possible metrics (e.g. Levenshtein distance). This will probably not get you very far. 
You can look at semantic similarity. You can use pre-trained word embeddings to map the words to a new vector space where you can calculate the distance between the word embeddings, e.g. with word2vec or other implementations. Alternatively, you can use a dictionary/corpus (e.g. https://www.nltk.org/index.html) that provides you a word taxonomy that allows you to compute semantic similarity between words via relationships like synonyms etc. See here for different approaches.