When I first started regularly practicing and performing music, as a kid in the school's concert band, our one-one-one evaluations were recorded on a cassette tape and submitted to the conductor. The first time you close yourself in a room, press a record button and play, your open up a whole world of new experiences-- mostly, disgust and self loathing combined with some moments of excitement and curiosity.
Particularly with small handheld tape recorders, some pinhole sized microphones don't necessarily capture what you're hearing when you're playing your instrument. Big surprise, right? I still use tape recorders because they're terribly simple to use, and you can instantly hear back your recording. This lo-fi method is still all you need for quick self analysis; listening back to hear of you were on tempo, if some technique you were trying out worked, or to critique (or save) a composition or riff for later work. If you don't have a bunch of crap from the 90s lying around, there are numerous "recorder" apps on every handset platform you can install on your phone, and it'll work just as well.
The bottom line is that in the moment, what you're playing doesn't sound the same as what people hear... they're not playing it. The process of composing -> playing (recording) -> listening (analysis) is invaluable and the best (quickest) way to improve. Better yet, you can use recording as a learning tool applicable to any type of practice. Record your scales, exercises, warmups as well as whole tunes and jam sessions with other players.
Once you've polished your sound up a bit, you'll probably want to showcase it to share it with your friends and others. Simplicity in the vein of an old cassette tape recorder exists in the online streaming/storage service of SoundCloud. You can directly record from your phone using the SoundCloud app, and some DAWs (Digital Audio Workstations) can even mix down your tracks and upload them directly to your SoundCloud account. Listening to your tracks on the SoundCloud web player offers an interesting comment feature; allowing you to pin comments to specific time stamps. Since the service allows you to host 6 hours of audio for free, having a private account is a great way to host an online library of your musical ideas and critiques.
If you don't often record yourself, next time you pick up your instrument to noodle around or practice, just press the record button on something before you do. Then listen back to it in a few days. You'll be surprised on how easily you'll instantly figure out what you like, what you don't' like, and what it takes to improve.