For sprays, just check the Ph level on the can. They always mention it. But depending on the type of glue, there is always possibility to damage the print while mounting it. Some of those sprays hold so well that if you get an air bubble (or worse, a print that sticks onto itself), you can pretty much forget the whole thing.
Mounting tissue is much more forgiving as it's totally dry. When I use some, I just use an old iron. Super easy.
First, I iron both the print (on both sides) and the mounting board. This removes all the humidity that might be left. I use some tracing paper on top of everything to prevent damaging the print.
Next, I cut the tissue to the size of the print. To make sure it stays aligned, I make a small X in the center of the tissue paper with the iron. The mounting paper is now held to the print. Next, I center the print on the mounting board. Once I'm centered, I lift the corners of the print and just tack the corners of the paper making sure my tacks are not on the edge. Now, the print is held loosely and I can look at it to make sure the job is OK. Once I'm satisfied, I put the tracing paper on top of the print and iron away.
I have an old pack of mounting tissue made by Kodak sometime in the 1970's... the stuff really lasts forever as long as it doesn't get wet.