You are wise to be concerned.
Typical ground points are either :
a) the green wire / 3rd prong in AC outlets which you lack,
b) metal plumbing pipes in older houses that do not use plastic fittings / lengths of pipe to connect the pipes (i.e. it should be metal all the way into the earth)
c) sometimes you can find the metal BOX enclosing an particular electrical outlet or lighting fixture is grounded, even if there is a 2-prong outlet installed in the metal enclosure. Basically there would have to be a green ground wire going to ground the box/enclosure or a grounded metal conduit screwed into the enclosure to provide a ground.
d) it is possible to buy what is called a "grounding rod" at a hardware / home supply store that is a few feet long thin metal pole that you push / hammer down into soft earth just outside of your home. For a temporary interior work surface ground point you then may take a copper stranded wire such as 18Ga or thicker (such as some $10 / 50' speaker wire) and run it through the door / window / cable TV egress / whatever out to the grounding rod where the wire is affixed (hose clamp, screw down terminal, wrap & twist, whatever).
e) if the area has a metal "natural gas" pipe it is possible to ground to that; give it a scrape to get the paint / dirt / rust off before you hose clamp / clamp / whatever the wire to the outside of the pipe. Needless to say, be careful not to break the pipe.
Also
a) If you want to invest in a proper setup that you can reuse in the long term it is possible to get an anti-static work-mat for the table which includes a wire lead or attachment point for one that goes to the ground. The cushion material of these mats is generally made to be ideal for laying delicate electronic components like a motherboard on and is superior therefore to laying them directly on a hard wood table due to scratching / pressure point issues et. al.
b) if you just have anti-static foam or some anti-static bags (really not the best choice) you can, rest your components on that surface and it'll be better than nothing but you should wear a wrist strap to ground yourself and be sure to pinch / touch the "work mat" often to keep it grounded as you work.
c) If you can arrange the use of an grounded 3 prong extension cord long enough to go to a verifiably properly grounded 3 prong outlet you can just use that to plug your PC PSU into, keeping the physical I/O ON/OFF switch on the PSU OFF (if it has a switch). This grounds the case of the PSU, and through it (once it is screwed into the PC case) the PC case itself is grounded. Then you can touch the PC PSU / chassis metal framework to ground yourself, and you can use these points as points of attachment for your wrist strap, work mat strap, etc.
Be sure the PSU is OFF just GROUNDED though. Some people make a special cord for the PSU that has cut off prongs so there is no AC power connections to the PSU but the ground wire is connected for grounding-only use during working, especially for cases where the PSU has no hard OFF switch.
d) If you want to do a lot of EE / tech projects you can get a "bipolar ionizer" ion blower unit that puts out precisely equal numbers (via an internal monitoring mechanism) of positive and negative ions and blows these over your work area. Thus any accumulating charges attract the opposite polarity ion and are discharged before a harmful build up occurs. You'd use this in CONJUNCTION with an anti static grounded work mat, wrist strap, grounded anti-static floor / chair mat, and grounding heel / shoe / ankle strap in a professional grade tech environment. Never use an ordinary household ionizer ANYWHERE near technology!!! It must be an electronics anti-static purpose ion blower or nothing at all.
e) As above you can get / improvise an leg (tuck inside your sock) / foot / ankle strap that is grounded, and get an anti-static floor mat with a grounding wire attachment.
f) You can also get a "spray" or floor / desk "polish" / "carpet spray" that is slightly conductive by design and helps reduce the chance of generating static, and even can help to discharge it to ground if it has a continuously applied path to a ground. Normal furniture polish / wax is bad and makes static problems much worse than just having a bare / dirty / raw surface.
g) Typically you'd want to clip the wrist strap, and foot/ankle strap (if used), and work mat strap(s) all together to a wire going to your ground point (pipe, earth rod, junction box / grounded outlet). If you don't have a good "ground point" to clip to then clipping off to metal on the PC case / PSU such as a bare metal fan / vent grille works well and is convenient for alligator clips provided that your PSU/Case is grounded through either the PSU+AC cord or through a distinct wire affixed to it.
h) You can use lengths of overlapping aluminium foil to cover your table work area over the part you'll be using most heavily, and then just secure a ground wire to it in a way that won't tear / fall off, or rest an earthed metal PC case frame / PSU frame on the foil to provide an earthing point for it.
i) For a fairly cheap / simple setup use a wrist strap, maybe some aluminium foil on the table, ground the PC case/PSU through a modified or normal 3 prong extension cord going to a grounded 3 prong outlet, and you're all set.
j) For another fairly cheap option that is a little more direct, run a long wire down to a grounding point (appropriate pipe / outlet / ground rod) as a temporary ground point for your wrist strap / mat / case / whatever. Remove the wire when done, again, cheap speaker wire / phone wire twisted pair / whatever can work for temporary uses.
k) The main thing with ESD is to avoid unnecessary movements in badly grounded work areas. If you scuff your feet across the floor, if you get up, walk, come back, if you rub your butt / back in a chair, if you rub stuff across the table / floor, etc. you can generate a charge easily. If you have all your tools, parts right in front of you within arm's reach so you don't have to sit / stand / move much then you'll make the process much safer even with no proper ESD protection. Try to reach out and "touch" everything in various combinations at appropriate places (esd packing foam, esd bags holding the parts, bare metal areas on cases / PSU, grounding eyelets on the motherboard, et. al.) to bring it all to a common potential.
l) try to avoid handling the electronics by their flat surfaces or anywhere there is a metal contact, PCB trace, component. Handle PCBs by the edges where there are no components / metal connectors to touch. Handle the CPU by its PCB edges, never touch the bottom contact rows at all. Hold cards only by their metal bracket and an insulated spot somewhere else like on the fan shroud or edge of the PCB. etc.