"I like jumping."
Translation:Я люблю прыгать.
When ‹ы› is stressed it's something like [ɨ], which would be like [i] ‹и› but a bit further back. Since in Russian this vowel sound occurs only after hard consonants—those that are not palatalized—it seems it is often causes <i>velarization</i> on the consonant.
Generally for us English speakers, just using [ɪ] and making sure the consonant is clearly hard might get the point across best.
But if you want to be a perfectionist, you can also try taking the [u] vowel and unrounding your lips, like you might do for Turkish ‹ı› or Vietnamese ‹ư›, if you happen to be familiar with those.
Here are four recordings of native-speakers pronouncing прыгать. https://forvo.com/word/%D0%BF%D1%80%D1%8B%D0%B3%D0%B0%D1%82%D1%8C/#ru
The ы sounds more like the -ee in "beep" than the soft "i" many are suggesting.
In using forvo.com, I have found that many of the pronunciations by the computer voice bear only a passing resemblance to the way the native-speakers at forvo pronounce words. Forvo is very useful in this regard.
I've been complaining about the fact that the microphone and speaker functions are all messed up, so that they don't work properly under Chrome, Edge, or Firefox on a PC Desktop/laptop. Now, I'm not so sure I should be complaining, since I don't want to learn how to pronounce words incorrectly.
Verbs generally do require a pronoun even in 1st person and 2nd person singular, unless you are going for a distinctly colloquial feel (even then, some places will almost always have a pronoun: for example, "Считаю, что ты дурак" is not technically wrong but very uncommon).
Usage of "Думаю" and, sometimes, usage of "Хочешь? ("будешь?") in questions are rather an exception. You may copy what you see in our course but it would be unwise to extend it to every single verb :)