A good SEO Agency or expert will provide you with full transparency as to what is going on with your site as well as the work that they are doing on your behalf. Typically the place most professional agencies will start is with a site Free Site Audit to determine the needs of the website and formulate a proper optimization plan that is based on your web site's needs.
This plan can consist of an initial clean up of your content and backlink profile if needed or simply a plan to move forward depending on what the audit finds. They will also conduct research into your industry and methodologies your competitors are using online to gain visibility.  Generally, keyword research is done to determine the best keywords for your site to rank on.
Depending on your agreed up SEO package, the SEO agency will then start to implement your plan which generally consists of adding quality content to the website and working on getting quality links to your site from other strong sites. While most agencies will have complete SEO packages available we always recommend a custom plan that is tailored to your site's needs for best results.