One thing that hasn't been mentioned!!!! Speed!!!
Correct speed during the whole descent phase allows you to be at the correct altitude at the right place in order to pick up and intercept the ILS. And if you are flying too fast the AP won't establish. The sim ATC do quite a good job in vectoring you to establish but if you are too high because you were flying too fast you will probably be overhead the airport instead of 10nm down range.
Let us say that you are in a jet cruising at FL350 at mach .84 using the GPS
ATC may call for an initial descent to say FL230. You must throttle back the engines to mach .64 but take into account the terrain ahead so that you know you will be clear at the point you anticipate reaching FL230.
Now at FL230 just how far away from your destination are you? Switch from Mach to IAS and fly at no more than 300kts. If less than 50 nm you should consider reducing to 250kts. In any case any instruction that takes you down to or below FL100 you must be at 250kts. Below FL100 reduce to 210knts.
After the initial descent ATC may ask you to change your heading. Switch the AP to HDG and the radio from GPS to NAV. Also at this point make sure you have tuned to the correct ILS frequency for the RWY in use
When ATC give you your final vector to establish (often including a new altitude) bring back your speed to 180kts. You should also at this point select first stage flaps.
Once the AP has aligned the a/c onto the vectored heading switch the AP from hdg to nav. Once the a/c has turned and is established on the localiser call the tower. Bring back your speed to 160/170 kts depending on a/c type and think about gear down and second stage flaps. The AP should also have captured the Glideslope You should establish at a point where the glideslope is above you. Now you can ask the AP to fly the GS as well. If the GS is not above you won't establish on the GS. At about 4nm out or the outer marker 3rd stage or full flaps depending on a/c weight type etc reduce your speed so that you are no more the 5kts above Vat at screen height. If the weather is gusty or you have a significant cross wind keep that 5knts component.
If you control your speed during the descent you make life easier for yourself and for ATC.
Vololiberista