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The first step is to decide on which keywords you want to rank higher for then plan out a good strategy and stick to it.
The usual seo strategy involves research keywords and writing content based on that keywords and then start promoting the website. Build relevant links from related websites this will carry a good seo value and helps in ranking higher.
Also try to keep up by posting content regularly this is what search engines love fresh content.
Once you take care of this content and link building then ranking will slowly increase and you will reach a good position if you are consistent.