Swimming, dancing and walking take 'avere', not 'essere'
Many English speakers learn an early rule of thumb: Italian verbs of movement take essere in the past, as in sono andato and sono arrivata. The rule is useful, but it misleads you with a large group of everyday verbs. Verbs that describe a way of moving or a physical activity, such as camminare, nuotare, ballare and sciare, normally take avere: ho camminato, ho nuotato, ho ballato.
English uses the same auxiliary for every verb (I have walked, I have gone), so it gives you no clue about which verbs belong in which group. Learners who see that a verb involves movement often reach for essere and produce forms like sono camminato, which sound wrong to Italians.
Think about what the verb focuses on. Verbs like andare, venire, partire and arrivare describe going from one point to another: leaving, arriving, changing place. These take essere. The verbs in this article describe the activity itself, meaning how you move, for how long and with what effort. The movement is something you do, like a sport or a hobby, and these verbs take avere.
A handy test: if you can naturally add per un'ora (for an hour) and the sentence is about the activity rather than about getting somewhere, expect avere. Even when a place is mentioned, as in Abbiamo camminato fino alla stazione, these verbs keep avere.
The basic walking verbs are camminare (to walk, the act of moving on your feet) and passeggiare (to stroll, to go for a walk). Zoppicare means to limp. Vagare and girovagare mean to wander or roam with no fixed goal, which is exactly why they take avere. Gattonare is what babies do on all fours, and strisciare is crawling close to the ground, like a snake.
Sports and dance verbs are the clearest cases: nuotare (to swim), ballare and the more formal danzare (to dance), sciare (to ski), pattinare (to skate) and surfare (to surf).
Viaggiare (to travel) and navigare (to sail) also describe an ongoing activity rather than an arrival, so they take avere too.
Because these verbs take avere, the past participle does not agree with the subject. A woman says ho ballato, not sono ballata, and a group says abbiamo sciato, never siamo sciati.
Notice the word normally in the rule. A few movement verbs, such as correre, saltare and volare, switch between avere and essere depending on whether a destination is involved. Those verbs follow their own pattern and are best learned separately. The verbs in this article are the reliable ones: with them, avere is the normal choice, even when the sentence mentions a place.
If the verb describes how you move or an activity you do (walking, strolling, swimming, dancing, skiing, skating, traveling, wandering), use avere: ho camminato, abbiamo nuotato, hanno viaggiato. Keep essere for verbs about going from one place to another, like andare, arrivare and partire, and never make the participle agree with the subject after avere.