Speaking at Mum's wedding advise?

Since you said "Mum", I'm guessing you're in UK, Australia or NZ. Generally here (I'm in Australia) the tradition is the speech goes a few minutes, like 3-5 minutes. (USA tends to keep them shorter as far as I can tell).

Generally you talk a bit about the bride (your mother), and maybe propose a toast. I find it best to (1) introduce yourself, (2) tell one or two funny/sweet stories, and (3) wish the couple well. The stories can be a little bit embarassing, but nothing humilating; and you should avoid mentioning anything she or the groom wouldn't want to here, e.g. romantic involvement with exes. (Though a passing reference to your father might be hard to avoid). If the stories involve her husband that's nice.

For more ideas, google "father of the bride toast" or "father of the bride" speech, because that is what you are effectively doing. Also take note of where the web site is based.

Once you have given her away your status reverts to 'son'.

Of course, as the Father usually gives away the Bride and then, in the Reception, has the Father/Daughter dance, that should be pretty interesting.

You are free to make any speech you want, though I do recommend two things.

1: Not embarrassing.

2: Use the KISS method. Keep It Short and Sweet.

There is another version of the KISS method. It is the 3 Ups.

1: To be seen, stand up.

2: To be heard, speak up.

3: To be appreciated, shut up. ;-)

Enjoy the day. It is, quite literally, one that will never come again for you.

I wouldnt get too serious with this.

I would just perhaps tell a short funny story about the couple or I would simply say that I am very happy for them, you can see how happy X is making your mother and you are happy to welcome him into the family.

Doesnt have to be a long thing like in the movies.