You will find that there are different customs (and even fashions) concerning tallitot (plural of tallit) in different congregations. A tallit is worn only for morning prayer, with the exception being all day throughout Yom Kippur (including during Kol Nidre). Even if no one wears a tallit where you pray on Shabbat morning, you may still wear one. If you don't feel comfortable, I recommend attending a Shabbat morning service in a synagogue in which tallitot are worn, so that you can try it and not feel conspicuous.