Probably the biggest barrier to new ukulele players who have never played a stringed instrument before - sore fingers!
Not much I can suggest for the pain. I'm afraid it's something you just have to go through, and its horrible. You will most likely get callouses or blisters on tips of your fretting hand fingers from the pressing of the ukulele strings, and you may also get cramps or aches in your hand from making chord shapes. The latter is also perfectly natural - you are making your fingers make and hold positions they are not used to, you muscles and tendons need to learn and strengthen.
I do have your sympathy, and would urge you to stick at it. It does get easier, and it would be such a shame for a beginner to give up ukulele because of sore fingers alone.
That said, I can provide you with some tips.
1. Practice! Obvious really, keep at it to toughen up those fingertips and strengthen your hand. if the pain is bad, try to practice for shorter periods but more often. Practicing uke only once a week will make it a long hard slog!
2. Find other strengthening exercises - some people swear by those grippy gadgets that mountain climbers use to strengthen their fingers, but those squeezy stress balls work well. Practice your gripping by squeezing these whenever you are not playing your uke. A friend swears by kneading bread dough as a good exercise!
3. Stretches - as well as building strength, you need your fretting hand to be flexible. When ever you are 'not playing your uke, try to introduce finger stretches into your day as often as possible
4. Leave the blisters alone! - you may well get blisters appearing on your fingertips which are both unsightly and sore. Don't burst them or pick them! Players of any stringed instrument build up callouses of harder skin on their fingertips that prevent this happening very often. Resist the urge! A tip I heard on this is to dip your fingertips in surgical spirit a couple of times a day for 10 mins or so- this stuff hardens skin. Also, don't be tempted to apply plasters and then play, they will affect your learning and accuracy in placing chord shapes.
Its really just about breaking through the barrier, and when you do, you will forget the pain and hardly feel the strings as you play.
Keep at it! The ukulele is worth it!
There is a beginners guide to finger stretching exercises - here