That's awesome! Your pictures and videos are always saved to the camera roll (Photos App) on your phone for just this purpose. Your pictures are yours, and we encourage you to use them however you like! Read on about how to find your pictures on your phone.
Finding Recent Pictures
First, open the Photos app. Your iPhone offers a wide variety of ways to browse the pictures on your phone, but for recent pictures, the camera roll album is convenient. Simply tap the "Albums" button. If this is already highlighted (blue), you can skip this step.
Next, find the "Camera Roll" in the list of albums. You may need to scroll your list by swiping up from the bottom of the list if it is not video. (Pro Tip: See pictures instead of albums? Check the header bar -- if it says "Camera Roll," you can skip this step. Otherwise, tap the "left" arrow in the top-left corner of the screen until you see a list of albums.)
Now, you should see a list of pictures. If you do not see the pictures you are looking for, scroll down the list by swiping up from the bottom of the list. The camera roll is arranged from oldest (top) to newest (bottom).
Finding Older Pictures
If you have a lot of pictures on your phone (or you're looking for ones that are a bit older), the camera roll might be a difficult choice for the task. Instead, it might be easier to locate your images in the "Moments" view. Tap on "Photos" in the lower left. If this button is already highlighted (blue), you can skip this step.
This will bring up a list of images separated by date and location. Swipe down from the top of the list to scroll through older pictures. If your screen does not say "Moments" at the top, see "Other Views" for how to find the moments view.
Pro Tip: Other Views
The "Moments" view is not the only arrangement your phone offers for viewing your pictures, even if "Photos" is correctly highlighted in blue.
If you tap the left arrow in the upper-left corner while viewing your moments, you will reach the "Collections" view. This looks like a zoomed out version of the moments view, with much smaller pictures separated by date and location. (See below.) To get back to "Moments," quickly tap twice any blank part of the screen which is not part of a collection (an example is circled in red below.)
If you tap the left arrow in the upper left hand corner while viewing "Collections," you will see your photos sorted by "Years." This looks like an even more zoomed-out version of "Collections." You can return to the "Collections" view by quickly tapping twice on any blank part of the screen which is not part of a year (an example is circled in red below).
In summary, there is a hierarchy of collections. From most zoomed-out to most zoomed-in, the hierarchy is "Years," then "Collections," then "Moments", and you can move between the levels of the hierarchy by double tapping to "zoom in", or tapping the left arrow to "zoom out." (Pro Tip: You can also "zoom in" by tapping the pictures of a collection, though this can be difficult with larger fingers.)
Viewing a Collection
While viewing "Moments," "Collections," or "Years", if you tap on the collection's header (outlined in red below), you can see a summary of that collection, including photos, videos, people, and other "related" photo/video stuff.
To "zoom out" from this view, simply tap the left arrow in the upper-left hand corner.
Viewing a Picture
While viewing a moment or a collection, if you tap on a picture, you will be able to see that picture in "full screen." The other pictures in the same collection (or moment) will be visible along the bottom of the screen. If you swipe left or right above the large, central image, or tap one of the pictures at the bottom of the screen, you will be able to view that picture in "full screen". Tap the left arrow in the upper-left hand corner to return to viewing the collection.