A toddler's first library visit does not need to include a class, a large borrowing stack and a complete tour. It can be a short introduction to a place you hope to use again. Check the children's area's hours and any registration requirements before going, then choose a time that reasonably suits your day.
Explain the visit simply: you will look at books together and may bring some home if you have arranged borrowing. Avoid promising a particular book unless you know it is available. A familiar title can be helpful, but discovering the shelves is enough of an activity for the first visit.
Find the children's area and choose a small place to begin. Sit with a few suitable books rather than asking the child to select from an entire room. They may spend time looking around or return repeatedly to one picture. You do not need to turn the visit into a test of whether they enjoy reading.
Use clear directions about handling books and moving around the room. Show what to do with a book when finished and ask staff where items should be left. Library arrangements vary, so do not assume you should reshelve everything yourself.
If a story session is underway, find out whether joining is appropriate and whether registration is required. Watching briefly may be enough. Leaving a group activity when it is not working for the child can be a sensible decision, not a failed visit.
Borrow a manageable number if you are ready to do so. Keep library books in a recognizable place at home and note the return or renewal date. This makes the next visit easier and prevents the new routine from beginning with a search through every toy basket.
Leave before adding errands merely because you are already out. On the way home, mention one thing you noticed together without requiring the child to summarize the experience. A short visit that ends well can make the library feel familiar, which is a useful result even if you read only one book.