Could someone who hasn't had their period in 10 months and finally got it recently get pregnant right after their period and if ovulation is hard to figure out how will you know without buying a kit?

You would have to know the reason why you haven't had a period for 10 months. Do you have a problem or are you usually this long in your cycles? You could watch your cervical mucus to judge ovulation. Your cervical mucus is usually white-cream in colour and sticky when you are not fertile. As you come into ovulation, the mucus turns clear (like raw egg whites) and is smooth and stretchy and slippery. You should find that it stays this way for around 5 days before drying up again. The general feel of your vagina area during this time will also feel quite wet.