Firstly you cannot use ADSL on a prepaid system, so explain to her that you need to convert it to a normal phone service.
Secondly , Telkom does allow a Technician onsite to sort you out (don't know if any free installations but just enquire at your local Telkom office) and all should be good.
As long as the computer is running XP/Vista (God forbid) or Windows 7 and has a network port then you should be fine.
Perhaps before setting up the internet, get the machine looked at, make sure there is antivirus (Microsoft Security Essentials 4.0 is free) and works great.
As far as connecting the PC for wired internet, its just a matter of connecting the network cable (included with your modem) to your pc's network port. Most come with a setup CD that asks you to fill in your details.
If you want to go the Self Install route, there is no harm and we can assist you every step of the way

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Oh and don't take a contract, go month to month. I would normally recommend Ti for your iSP but get the ADSL line from Telkom and take a DATA-Only account from MWEB as their 1MB account is now R199. They do have a slower speed account for the same price but come June this year, upgrades will change that 384 to 1MB. More info on this will be coming around just check the front page for news.
So in essence
Check your PC for any troubles you think your mum may experience (popups etc)
Check to see if there is a free installation for a tech to come onsite otherwise take the self-install option and we will gladly walk you through the process
Take your ADSL line from Telkom and your DATA ISP account with MWEB
Cost breakdown if i am right should be something along the lines of
ADSL Line Rental 1MB speed - R289.00 (Telkom's price)
Analogue Line Rental - R139.97
1MB Data account (MWEB) - R199.00 (uncapped account)
A Modem/Router -
TP-Link TL-W8961ND @ R534.66 incl vat (pricing on their website is excl). This is a recommended model from members on the forum and is cheaper than Telkom's range starting from about R899.00
TOTAL Monthly Cost = R627.97 & R534.66 for the modem once off so first month = R1162.63 (note dbg can deliver so do check with them unless you can pickup).
For more info on above, check the links below
Telkom's DSL Cost breakdown
MWEB's R199.00 product page
Just had a look on the site, Telkom will charge for coming out, rather take the Self Install route and we will help ye out

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/hope i didn't miss anything