I am having my first baby and have been told to baby proof my house. What would you recommend?

It is essential. Baby and child proofing your home will prove both a sanity saver and keep your baby safe. Once your baby becomes mobile (rolling, crawling, walking), she will be curious about everything and i mean everything. And? It will all go into the mouth at first. Keep choking and toxic hazards out of reach, plug those outlets, gate those stairs, and keep re-evaluating your home child proofing needs.
Think like a baby. Crawling, toddling, or walking - if they can get into it, they will. Anything electrical, poisons, drugs, cosmetics, paints, breakable stuff, sharp edges - you name it; they'll find it. And, they'll figure out how to get into it or get hurt by it. Get down on hands & knees (or lower) and look from their viewpoint. Remember: prevention beats treatment!