Everyone has a favorite guitarist that inspired them to start playing and wish they could play just like them. Emulating the style of your favorite player takes a lot of study and sometimes intense practice.
You can start by looking for commonalities you can find across their catalog of songs. Just listening closely is the first step to take. Listen for rhythmic patterns that happen repeatedly. These can be as obvious as strum patterns that are used in more than one song or as subtle as rhythmic fills that happen in transitions between chords.
Often an artist will use the same techniques in more than one song but apply those techniques differently to create something that sounds unique. Just try to recognize them by ear at first. No need to dig deep that you try to analyze them through playing. Remember you should be looking for things that so obviously sound the same that no further analysis is necessary.
Check out some early AC/DC music to find an example. "Ride On" and "The Jack" have both similar rhythm, tempo, and chord changes. Stevie Ray Vaughn's use of 7th and 9 chords as applied to a blues progression in many of his songs is another example. Tom Petty's "Even The Losers" and "Runnin Down A Dream" have a similar feel rhythmically.
All of these artist use similar subtle fills as well. Angus Young often uses blues style turnarounds to a rock context. Stevie Ray Vaughn uses tasty pentatonic based licks and quick chord turnarounds. Tom Petty adds memorable accented strums.
When you’re done finding the obvious stuff dig more to find melodic patterns or similar single note figures among songs. These usually consist of some sequence of notes, in simple terms how the song "goes" or it's main "riff". A really good example of this is Metallica songs. Take "Seek and Destroy" and "For Whom The Bell Tolls". Each has a memorable melodic pattern for the intro. Van Halen's "Panama" and "Unchained" intros are a good demonstration of similar riffs. If you are fan of more mellow stuff listen to "The Chain" and "Landslide" by Fleetwood Mac.
Next we focus on the solos. Here "signature licks" and what you want to seek. A signature lick is a lick that is often used by an artist, sometimes played at a different tempo but the same notes in several different solos. Eric Clapton has a catalog of such licks he has been using since his early days in Cream. You can even find the melodic lick used in the "Wonderful Tonight" solo played at different tempos among other songs such as "Prentending". Van Halen uses the same speedy lick in both "You Really Got Me" outro and "Hot For Teacher" solo. Angus Young uses a blues/rock string bend lick in "Back In Black" and "You Shook Me All Night Long" and a similar speedy pentatonic lick in several other songs.
Lastly you can look for what I like to call articulation techniques. These are the small details of how a player picks the strings, uses vibrato or mutes notes. For example Billy Joe of Green Day has a percussive attack on the strings when he picks whereas Yngwie Malmsteen uses small smooth pickstrokes and you can really hear the difference. Keith Richards of the Rolling Stones uses a lot of dynamics in his picking. Glen Tipton of Judas Priest has articulates his notes masterfully.
When you study you favorite guitarist's style take all of these things into consideration to break down their style and things should progress nicely.