There are multiple ways of flying the F28 onto an ILS approach, but let's assume that you've got the aircraft on autopilot to a decent point to intercept the ILS.
Let's say that our generic ILS has a frequency of 110.10, is on a heading of 090 and has an intercept point 10nm from the runway at an altitude of 3000ft.
Let's also assume that you're 15 miles out and are tracking to intercept the localiser at the classic 45 degree angle.
You have the autopilot engaged (A/P and DAMPING switches at the rear of the pedestal switched on). The Mode Selectors in the glareshield are set to HDG and HT. The heading selector is set to 045 (our 45-degree intercept course), and the autopilot is holding 3000ft altitude.
If you've been flying using the FMS for navigation, make sure the Source Selector (just above the airspeed indicator) is set to NAV (green light), so the autopilot takes its data from external sources, not the FMS (that answers your last question - yes you can bypass the FMS and fly an ordinary ILS).
Make sure NAV1 (the left-hand tuner in the glareshield) is set to the ILS frequency (110.10 in this case) and the NAV1 Remote Datum Selector is set to the ILS course (090 here), with the NAV1 button selected (white light illuminated).
Then push the BEAM and GLIDE mode selectors. This will arm these modes to capture the Localiser and Glideslope respectively. In terms of button-pushing this is all you need to do.
The Progress Annunciator lights for VOR LOC and GLIDE SLOPE (above the altimeter) will show yellow lights.
You can also turn the Flight Director to GS AUTO, which will make the FD bars track the ILS, but that's only to add to the pilot's awareness - you can fly ILS approaches with the FD entirely off if you want.
In this situation, the aircraft will intercept the Localiser first. You'll see the purple bug (showing the bearing to the localiser beam) move towards the yellow course needle (showing 090) and as it gets within about 5 degrees the yellow course needle will start moving across the HSI.
As it passes one dot of deviation (to the left, in this example), the HDG mode will automatically disengage (leaving just BEAM), and the VOR LOC annunciator will switch to green, showing the autopilot has intercepted the Localiser signal. The aircraft will turn onto and track the Localiser. (If you're close to the threshold and/or flying fast, you need to monitor the rate of capture and may need to use the Heading selector to turn in earlier, otherwise the aircraft tends to overshoot).
As the aircraft establishes on the Localiser, you should notice the Glideslope deviation bar moving down the scale. As it reaches the middle of the scale, HT mode will automatically be disengaged (leaving just GLIDE) and the autopilot will pitch down to follow the Glideslope.
With BEAM and GLIDE engaged, the aircraft will track the ILS until you choose to disengage and complete the landing.
One procedural thing - just for accuracy that has no real relevance in the sim - that procedure above is for Category-I approaches. For Category-II approaches in the F28, you should set the ILS frequency on the NAV1 tuner but then press the APPR button on the Remote Datum Selector (rather than NAV1) so that both white lights illuminate. In APPR mode the NAV1 tuner controls both NAV radios, so both are receiving the ILS frequency. The NAV1 signal would be displayed on the captain's HSI and the NAV2 signal would be on the F/O's HSI. All being well, they would be the same but it allows the crew to cross-check and monitor the signal. Under Category-II limits and flown this way, you can (if the conditions and approach allow) let the F28 fly itself all the way down to 50ft before disconnecting the autopilot and carrying out the flare and landing. The proper thing to do is to set the NAV2 tuner and course selector to the airfield VOR and missed approach course before hitting APPR - NAV2 will work the ILS in APPR mode, and then if you go around you just have to hit the NAV2 button and the HSIs will immediately show the missed approach course.
This isn't at all needed in MSFS where ILS signals are always perfect and the radios never fail, but it's how it was done 'by the book' and it can be done this way in the JF F28 if you want to be authentic/pedantic.
