Historical linguistics is the branch of linguistics concerned with discovering the relationship between languages and understanding how languages change over time. Historical linguistics and genealogy have many things in common. Both are concerned with relationships and both require a systematic and thorough examination of the available evidence and careful argumentation. They also both share a fascination with maps and trees. Understanding something about historical linguistics can also help in genealogy.
Leveraging your knowledge
Understanding how languages are related can help you leverage the knowledge you have in one language for research in a related language. Like people, languages are grouped into families based on common descent. Some languages are very closely related, while others are more distantly related. More closely related languages typically have more words and structures in common. You can use your knowledge of English to help further research in other Germanic languages. Many of the words in German, Dutch and Scandinavian languages will be immediately familiar to speakers of English. You should be able to guess the meanings of verbs in German like beginnen, bringen, enden, fallen, helfen, kommen, kosten, landen, lernen, senden, springen, starten, wandern, and many others. If you know two languages are related, don't be afraid to guess the meaning of words that look familiar. You may make a wrong guess, but more often if you take the context into account you will be right.
Another important lesson from historical linguistics is that languages are often related in systematic ways. For example, the letter d in German often corresponds to th in English. You can use knowledge of this to help guess the meaning of words like danken "thank", denken "think", die "the", das "the or that", drei "three", dreizig "thirty", dein "thine", etc. Other examples of such systematic relations include German v and English f (vater and father) and German t and English d (tag vs. day). These difference are due to a combination of changes occurring in only one language and spelling conventions.
There is more to relationships than genetics
Another important lesson from historical linguistics is that languages are related in ways beyond common descent. Many of the similarities between languages are due to borrowing. Through the Roman Empire, the Catholic Church and science, Latin borrowings are found in every European language and most widely spoken languages of the world. Another language that had a huge influence on English is that of French. William the Conqueror and the Normans brought the French language with them fundamentally changing the English language. It is hardly possible to write a paragraph without some Latin or French borrowings. The science fiction writer Poul Anderson illustrates this by attempting to explain atomic theory in his essay titled "Uncleftish Beholding". It is useful to know which languages belonged to the same "community" and influenced the language you are working with.
In genealogy it is also important not to become to wrapped up exclusively on our ancestors blood relationships. They were also parts of communities and networks of friends which may yield evidence about our ancestors' lives.