That's nice!
There's no formal tutorial on the 244, but the operator's manual is very good. Being a machine that's on loan, purchasing a manual might be excessive.
Here are some basics:
On the back there are Access-Snd/Rcv jacks, and they should be jumpered together from send to rcv on all channels, 1-4. (WITHOUT THESE POINTS JUMPERED PROPERLY, THE MIXER WILL NOT WORK).
Turn the Trim control all the way to the Line position, (left). That's minimum preamp gain.
Turn the master fader and each channel faders to 0 to start initially.
Set the Tape Cue section's volumes to "0", for starters.
Set EQ Gain to "0", (middle position).
Set AUX Send to "0", (fully CCW). Set Aux-Select to "Off".
Set (main) Pan control to center.
Plug your mic or instrument into inputs 1-4.
Set the Input Select to Mic/Line position.
While playing or speaking/singing into mic, rotate the Trim control Clockwise, until the OL LED starts to flash, then back it off a hair.
Set the Master fader to the 7~8 position, the shaded area.
You should be able to push the Channel faders up to about the 7~8/shaded area at this point, too.
Set the Rec-Function to [1] and [2] "Ready" position, (both switches to the left).
Set the headphones either to Buss or Cue,... it doesn't really matter (AT THIS POINT). Headphone level will be about "3" for comfortable listening.
You should be able to hear the inputs in the mixer over the phones. Apply EQ or efx as necessary at this point, user's choice. (ADJUST LEVELS AS NECESSARY).
Setup this way at this point, you should be seeing the input mic/line signals on the VU meters for Buss-Left and Right, which is the signal you're feeding to your record-ready Tracks 1 and 2. If you vary the Channel Pan control left and right, you should see your input signal route left and right on the meters, which would correspond with routing the input signals to the "left-buss" tracks (1/3) or the "right-buss" tracks (2/4). The fundamental idea of using the mixer "pan" and the "rec-funct-select" controls in combination is the way you route inputs/channels to tape/tracks, in varied combinations depending on your situation. There is also a "4-Direct/Simul" recording mode which is pretty simple, in that it routes each input's signals directly to it's corresponding tracks, and records them in 4-tracks/simul down to tape. This was a vast improvement over the original Portastudio, which enabled 4-live-to-tape recording, or even dubbing 4-simul from another Portastudio, for backup purposes. This 4-simul-record function is something that's taken for granted these days, but the 244 Portastudio was the first cassette machine to have that feature. It was a huge boost in utility of the unit, and therefore it's been carried down to all the subsequent high-end Portastudios, ever since.
Press Record and Play, and record either to Track 1, 2, or 1 & 2 as a stereo pair, (your choice).
Once you've recorded your first tracks, rewind and play back without changing any of your inputs or main-mix settings. To bring the previously recorded tracks up in the phones, you'd use the "Tape Cue" section (HEADPHONES SET TO CUE). This gives you the previous tracks from tape mixed in the phones with the live/main mix, simultaneously. It's essential to become familiar with the "Tape Cue" section when you're overdubbing. Rotate the Tape Cue's gain and pan as necessary to get a good mix the the phones.
When your 4 tape tracks are filled up, you may then do a full "remix" by clearing the board of inputs and setting the Channel Selects 1-4 to "Tape". This brings the tape tracks through the main-mix section, so that you may apply EQ and efx as necessary, and use Pan to achieve a final stereo mix. Using this remixed stereo mix from tape, you'd then dub from your Portastudio to a "standard" cassette or even your 'puter to make CDs of your mixes.
I'm sure I've forgotten something, but others may come along with supplemental information.
I'd even assume that you've probably figured out the 244's operation, in the single day since your post.
Maybe offer your friend $40 for the 244, and then go buy a manual too. It's one of the better equipped and better sounding Portastudios in the entire line,... despite it's age. Some of my best productions were done on a 244, back in the day and well into the present.