Welcome to Knitting Help, Miss Tiggy! Don't be scared, we all had to learn some time and it's like learning a new language...so confusing and makes no sense at first. Thank you for telling us what you're making..that is always helpful and if you can include the pattern name and a link if possible that's always good, too. If you can't link you can type out a few lines of the pattern just like you did.. perfect.
When you increase IN the next stitch you'll usually be doing what is known as a KFB (knit front back). There is a video for it under the increase videos linked above. You knit into the stitch like normal, but don't take it off as you usually do. While it's still on the needles you knit into the back of the stitch, wrap the yarn and pull it through then take the new stitches off like normal. It's clearer once you see the video. Just do the increases as the pattern tells you. When you are done with that row you should have 141 stitches.
I recommend you put markers at the increases if possible. I don't have a link to the pattern so I can't see how they are done, but markers make it much easier to remember where they are in most patterns. If they are always random then it will be harder so you need to keep track of your stitch count.