how to chase a girl

Express interest.  This can be done in the following ways,  not necessarily in this particular order.

- small gift.  The key is something with small monetary value but stands out amoung its peers.  For example Starbucks coffee or California dates, not regular coffee or a packet of cheap snacks.
- small favour.  Again the key is small.  Proof reading an university assignment is a good example, completing the whole assignment is overdoing it.
- compliment.  Be specific, be creative.  For example 'you are pretty' is no good; 'you have pretty eyes' is not bad ; 'some girls have looks but no style, some girls have style but no looks,  I think you have both ' is amazing.  Saying a good one once is enough to have a permanent effect. Saying it too often backfires and makes you a pandering wimp.

And then what?

If a girl digs you she will start the interaction. Give her the pleasure to do the rest of the work.

If not it doesn't matter what else you do,  it won't change anything.  Find another target, rinse and repeat.