No Pain no Gain
Chords are notorious for causing pain in fingers and it's a big factor in guitar abandonment. The pain of pressing down strings will go away with regular practice. Just start with E, A & D chords. Play these until you can switch back and forth smoothly. Eventually, you'll have calloused fingers and clamp onto chords with ease. If a steel string guitar is still too painful to play you may be better suited to a different guitar. The classical guitar has nylon strings which are much easier to push down. Electric guitar strings are even easier to play, but don't plug it in while practicing - an electric amp is too distracting for someone simply trying to learn the basics.
Tap your foot
If you can tap your foot in time, then you can absolutely strum the guitar in time too. The key here is to always be tapping your foot, but let it be your master clock. You can trust that foot, so go with it and never miss a beat. This can at first feel awkward, but it's no different than riding a bike. Once you get the hang of it, you'll always have the rhythm. The common problem of stopping and starting over in the middle of a song comes from overthinking. Follow the foot and if your chords are buzzing keep strumming anyway. Don't let a bad chord stop your flow - play right through even if you have to play bad chords. Just keep the tempo and keep strumming.
Get a Tuning Fork
Remember these? You smack it against the dresser and it responds with a perfect tone. Not only does it help tune the strings, but also your ears. There are a tons of digital tuners out there, but they have created a generation of lazy guitarists who tune by sight. These tuners get the job done, but when looking at the colored strobes, the ears can become disengaged. The tuning fork forces critical listening, and activates musicality. This simple tip alone can bring a rapid advancement in playing for everyone from students to professionals. Seriously, grab a set online or at the local guitar shop. Another option is to use an online guitar tuner as a virtual tuning fork.
Learn That Song
We all have one. That song that we know all too well and can be played inside your head, from start to finish. Commit to learning a song or two and playing it all the way through. Start by finding the chords online or in a tablature book at guitar center. After you can play the chords, it's time to play along with the actual song. Playing guitar is 90% listening and 10% doing. While the song plays, just strum along lightly while keeping focused on the song. The trick here is to improve your listening and then use it to self adjust. Music is a subtle art whether your thing is black metal or ragtime.
Turn on the TV
With the television turned on and muted, play the guitar while watching your favorite show. This will improve another subtle guitar skill called Intuition. Simply knowing those chord changes (without looking) will bring fluidity and comfort on the instrument. Getting your eyes off the instrument, while playing it, brings familiarity.
Since those E, A & D chords may get boring, a subtle change to the fingering can make things very interesting. Take the middle note out of the E and A chords for a more bluesy sound. Learn all the variations of these chords and you'll soon be improvising and writing tunes. Grab a guitar tuner that suits your style.
After finding your way around standard tuning on the guitar, consider trying an open tuning for a while. The guitar will instantly sound deeper and heavier. All of the chords you've been practicing will sound completely different. Explore a bit in open tuning and you'll feel like a vast horizon opens up right in front of you. Make some music.