I'll assume that you've performed general maintenance & housekeeping on your present 128 GB SSD and you're satisfied that the present total contents on that disk are reasonable in that it meets your objectives.
So as to the cloning of your present SSD to a considerably larger SSD...
I'll assume that you're pretty much thinking of a one-shot disk cloning operation and not interested in also using a disk-cloning program as a tool for maintaining frequent comprehensive backups of your system. I mention this because the program I'll recommend to you is a freebie. It's not the program I recommend should you desire a disk-cloning program that can also be used for routine backups of your system. But that program is a commercial one and costs $49.99. I find most users loathe to purchase this type of commercial product when there are so many free disk-cloning programs available. More's the pity...
Anyway the program is Macrium Reflex Free. You can download it from...
http://www.majorgeeks.com/files/details/macrium_reflect_free_edition.html
It's a reasonably easy program to use and seems to do the job based on my (admittedly) limited experience with it. Here are some instructions...
Before opening the Macrium Reflex Free program and undertaking the disk-cloning operation close any open programs and remove or uninstall all storage devices, e.g, flash drives, other external USB devices, from the PC other than the source & destination disks that will be involved in the cloning operation. It is unnecessary to uninstall any fixed HDD/SSDs.
The destination disk can be installed either as an internally-connected drive or as a USB external HDD/SSD.
1. With both the source & destination disks connected, boot to the source disk & open the Macrium Reflex Free program.
2. The opening window will reflect the two disks. The destination disk will be listed below the source disk. Both disks should be check-marked (default).
3. Click "Clone this disk".
4. On the next window click "Select a disk to clone to...". The destination disk should appear in the window.
5. Click on the graphic of the destination disk, then click Next.
6. The Clone Summary window will appear indicating that the source disk will be copied to the destination disk.
7. Click Finish.
8. The Confirmation Overwrite window will appear requesting confirmation of the disk-cloning process.
9. Click Continue...
10. After the destination disk is successfully cloned ensure that it is connected to the motherboard's first SATA connector which will be designated either SATA 0 or SATA 1 depending upon the motherboard's designations. I'm assuming, of course, that the cloned disk is to serve as the PC's new boot drive.
So as you can see it's a relatively simple & straightforward process and you shouldn't have any problems with it.
Don't know if you've decided on the make/model/capacity of the larger SSD but if you haven't my advice would be to purchase the larger-capacity SSD if you can swing it $-wise. As to make, it's hard to beat the Samsung 850 Pro. I've had experience with about a dozen or so SSDs and greatly prefer that Samsung to all the others. I've found nothing faster, but of course you'll pay a premium for that model. And truth to tell I have to admit there's not an enormous difference in real-world terms with virtually any SSD compared to another SSD.