First off, if you ever need any help using Nintype, check out the Reddit wiki. It is a little outdated, but the developer of Nintype almost never removes features.
Assuming that you have completed the tutorial, there is one thing you should do immediately. Hold the space bar, hit the yellow settings icon, scroll down to sounds, and enable "haptic feedback".
By default, there are 2 different modes, slidemode and peckmode. You can toggle between the two by tapping the icon in the top right corner.
Slidemode uses autocorrect and sliding gestures, this is what you will be using for most of your typing. Peckmode is made more for typing URLs. It does not feature any autocorrect, and also displays more buttons such as shortcuts, @, #, and common domains.
You can enable a third mode in settings, called stockmode. This mode does not allow you to slide your finger to swipe words, but still has autocorrect. Sliding your finger can still perform different shortcuts and actions.
Backspace opperates a little different with Nintype. When you press backspace, the whole word will be deleted at once. If you want to delete only part of the word, slide left on the backspace key. The more you slide, the more will be deleted. If you go too far, you can slide back right to restore deleted text.
The topbar will show the history of what you have typed. If you realized you spelled something incorrectly, you can tap the word to see other suggestions. In this menu, you can tap the large shift menu to quickly change capitalization.
A quick way to change capitalization is to slide left or right on the spacebar. This will move the cursor. While sliding over a word, while continuing to hold space, just press the capitalize button.
Slide your finger up on numbers on the top row of the keyboard to type the small numbers shown. Also, while in the number page, you can type out math equations, and a calculator will automatically come up.
Instead of giving you my recommended settings, I feel you should just look through the settings on your own and mess around. It's much more fun this way, and is a great way to figure out what you think will work for you and what won't. Settings can be found in the spacebar menu.