Take time to consider every possible synonym and don't stop until you are sure that a publication that does not contain any of your selected synonyms can not be relevant for your question. Avoid very common words with many meanings. Be aware that some terms have different meanings in different contexts, and that the same phenomenon can have different names in different subject areas. You have to include all your synonyms in the search, keeping in mind that most databases will do exactly what you tell them, and only what you tell them, and they do not know anything about synonyms or natural language. If you write "horse" in your search strategy, it will not find ponies, racehorses, thoroughbreds, foal, mare, stallion even though all these words also relate to horses. In some databases the search engine will not even find the plural "horses".
Specify exactly how your search terms should relate to each other. There are a few quite general syntax rules that are interpreted in the same way in most databases, see Search tips. When in doubt, different databases do different things. The easiest example is if you write two terms after each other with no Boolean operators involved, for example horse therapy, one database could interpret this as meaning horse AND therapy, another could search for horse OR therapy, a third might see it as a phrase, "horse therapy". The results signify totally different concepts. Always be as specific as possible to help the database do what you expect, and to ensure that your search is interpreted in the same way in all the databases you want to use for your search.
Look out for "user-friendly" interpretations in the database functionality. Some new tools, search engines and databases with a high ambition of being user-friendly, and also databases relying on natural language processes rather than assigned terms, will try their very best to help you with creative ideas about what you would like to know. This can give you lots of inspiration in your synonym-finding work! But it is a problem for the transparency and reproducibility that you are aiming for. Worst of all in this context is that some sources keep track of what you have selected in earlier searches (eg. Google does this very efficiently) and will do a relevance sorting which shows you mainly the things that you already know. This is more or less a disaster for the objectivity needed in systematic searching.
Consider the hierarchy of your free terms. A simple term might capture what you need, and there is no need to add extensions for that term unless you are looking for the extended term only, e.g. "horse" covers both "horse therapy", "horse riding" and any other expression containing the word horse.
Iterative method: in the articles retrieved in your first search attempt, you will probably find more relevant terms in the title, abstract, and keywords. Run a new test search with these terms included. If this captures even more relevant articles, try to identify more terms in them. If you already from the start know of some publications that are essential for the research questions, so called "golden articles", check if the search retrieves them. If not, and the articles are available in the database, you need to adapt your search further to capture the research question in your search. The "golden articles" can be a great help to find important search terms. Keep testing in one of the databases you will use, note the number of hits that each new term contributes, and repeat until no new relevant publications are retrieved. The film below is showing how to test your search terms in Web of Science .
Checking your search terms in a database
Consult subject experts - it can be as easy as asking your colleagues.
Talk to the library. Many guidelines for systematic searching explicitly recommend discussing your search query with an experienced information specialist. Databases and their search rules are constantly changing, and there are tips and tricks that are special for each one of them. Information specialists may not be as familiar with the terminology in your research area as you and your colleagues are, but have more experience when it comes to databases and search strategy design.